Find The Derivative 9E^3X – Find The Derivative F(X)=9E^(

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Find the derivative of the function: 0 votes

f(x)=(4-e^-3x)^3?

derivative-of-a-functionaskedNov 18, 2014in CALCULUSby anonymous

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Please log in or register to add a comment. Please log in or register to answer this question. 1 Answer 0 votes

The function f(x) = (4 – e-3x)3

Differentiate with respect to x.

Apply chain rule in derivatives.

Apply the formula d/dx(ex) = ex

d/dx(xn) = nxn-1

d/dx(x) = 1

d/dx(constant) = 0

f”(x) = 3(4 – e-3x)2 (d/dx)(4 – e-3x)

= 3(4 – e-3x)2 (3e-3x)

= 9e-3x<(4 - (1/e3x)>2

= 9(1/e3x)<(4e3x - 1)/e3x)>2

= 9(1/e3xe6x)(4e3x – 1)2

= 9(1/e9x)(4e3x – 1)2

f”(x) = 9e-9x(4e3x – 1)2.

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