What is the derivative of #(2x-3)^5#?

1 Answer
VNVDVI
Mar 30, 2018

#10(2x-3)^4#

Explanation:

Apply the chain rule, which tells us that #d/dx(f(g(x))=f'(g(x))*g'(x).#

For the function #(2x-3)^5,# we see it is a polynomial composed with an exponential function. So, the power rule is used to differentiate the polynomial raised to the #5th# power, and the fact that #d/dxax=a# to differentiate the polynomial #2x-3#

#d/dx(2x-3)^5=5(2x-3)^(5-1)*d/dx(2x-3)#

#=(2)(5)(2x-3)^4=10(2x-3)^4#

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