Problem 8
Question
Find the derivative of the function. $$ h(x)=2 x^{5} $$
Step-by-Step Solution
Verified Answer
The derivative of the function \(h(x) = 2x^5\) is \(10x^4\)
1Step 1: Identify the Power Rule
The derivative of a function in the form of \(x^n\) where \(n\) is any real constant is given using the power rule. The power rule is \(nx^{(n-1)}\) where 'n' is the power of x. In this function, \(2x^5\), 'n' is equal to 5.
2Step 2: Apply the Power Rule
Applying the power rule to \(2x^5\): derivative \(h'(x) = 5*2*x^{(5-1)} = 10x^4\).
3Step 3: Final Answer
So, the derivative of the function \(h(x) = 2x^5\) is \(10x^4\).
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