In: Math

# What is the Derivative of f(x)=(4x^7)^5

Find the Derivative of the f(x)

## Solutions

##### Expert Solution

Using the power rule and chain rule for derivatives subtract the exponent by 1 and the contsant to the front of the parentheses then proceed to do the same to the inside of the parentheses using the chain rule so what you derive inside of the parentheses doesnt change. (4x^7)^5=5(4x^7)^5-1=5(4x^7)^4. then do the inside of the parentheses. 5(4x^7)^4 *28x^6=5*28^6(4x^7)=140x^6(4x^7) so the final answer is f'(x)=140x^6(4x^7)

140x^6(4x^7)^4