Đang xem: Derivative 9e^3x
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Find the derivative of the function: 0 votes
derivative-of-a-functionaskedNov 18, 2014in CALCULUSby anonymous
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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