Question

Differentiate the function. g(x)=4x^(-3)(x^(4)-4x^(3)+13x-2) 

          Differentiate the function.
g(x)=4x^(-3)(x^(4)-4x^(3)+13x-2)
differentiate the function gx4x 3x4 4x313x 2 35623

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Differentiate the function. g(x)=4x^(-3)(x^(4)-4x^(3)+13x-2)
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Transcript

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00:02 So they asked us to find the derivative of this function here, x times either the minus kx.
00:10 So this is a pretty straightforward application of first the product rule, because we have a product of two functions for x, and then the chain rule to get the derivative of this thing.
00:22 So product rule, take the first term times the derivative of the second, plus the second term, second term times the derivative of the first.
00:32 Then here we need to use the chain rule, so i define u to equal minus kx.
00:43 So i have x from here, and then this is the derivative of e to the u to u times the u d x, which is minus k x prime.
00:58 And then the derivative of x is just one, so then this comes down here...
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