Chapter 3

If \(f(x)=(2 x+1)(3 x-2)\), find \(f^{\prime}(x)\) two ways: by using the product rule and by multiplying out. Do you get the same result?

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ y=5 \sin x $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(f(x)=2 e^{x}+x^{2}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$y=5$$

If \(f(x)=x^{2}\left(x^{3}+5\right)\), find \(f^{\prime}(x)\) two ways: by using the product rule and by multiplying out before taking the derivative. Do you get the same result? Should you?

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ P=3+\cos t $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(P=3 t^{3}+2 e^{t}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$y=3 x$$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ f(x)=x e^{x} $$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ y=t^{2}+5 \cos t $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(y=5 t^{2}+4 e^{t}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$y=x^{12}$$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ f(t)=t e^{-2 t} $$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ y=B+A \sin t $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(f(x)=x^{3}+3^{x}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$y=x^{-12}$$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ y=5 x e^{x^{2}} $$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ R(q)=q^{2}-2 \cos q $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(y=2^{x}+\frac{2}{x^{3}}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$y=x^{4 / 3}$$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ y=5 \sin x-5 x+4 $$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ y=t^{2}(3 t+1)^{3} $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(y=5 \cdot 5^{t}+6 \cdot 6^{t}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$y=8 t^{3}$$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ f(x)=\sin (3 x) $$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ y=x \ln x $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(f(x)=2^{x}+2 \cdot 3^{x}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$y=3 t^{4}-2 t^{2}$$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ R=\sin (5 t) $$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ y=\left(t^{2}+3\right) e^{t} $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(y=4 \cdot 10^{x}-x^{3}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$y=5 x+13$$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ W=4 \cos \left(t^{2}\right) $$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ z=(3 t+1)(5 t+2) $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(y=3 x-2 \cdot 4^{x}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$f(x)=\frac{1}{x^{4}}$$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ y=2 \cos (5 t) $$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ y=\left(t^{3}-7 t^{2}+1\right) e^{t} $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(y=5 \cdot 2^{x}-5 x+4\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$f(q)=q^{3}+10$$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ y=\sin \left(x^{2}\right) $$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ P=t^{2} \ln t $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(f(t)=e^{3 t}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$y=x^{2}+5 x+9$$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ R=3 q e^{-q} $$

Differentiate the functions in Problems 1-28. Assume that \(A\), \(B\), and \(C\) are constants. \(y=e^{0.7 t}\)

Find the derivative. Assume \(a, b, c, k\) are constants. $$y=6 x^{3}+4 x^{2}-2 x$$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ y=A \sin (B t) $$

Differentiate the functions in Problems 1-20. Assume that \(A\) and \(B\) are constants. $$ z=\cos (4 \theta) $$

Find the derivative. Assume that \(a, b, c\), and \(k\) are constants. $$ f(t)=\frac{5}{t}+\frac{6}{t^{2}} $$