How do you differentiate $x^1.7cosx$ ?

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Answer 1 · 2018-07-30T20:32:23

$d/dx(x^1.7cos(x)) = 1.7x^0.7cos(x)-x^1.7sin(x)$

This problem is an example of the Product Rule where

$f(x) = x^1.7$ and $g(x)=cos(x)$

Their respective derivatives are

$f'(x) = 1.7x^0.7$ and $g'(x)=-sin(x)$

The Product Rule states that

$d/dx(f(x)*g(x))=f(x)*g'(x)+f'(x)*g(x)$

Plugging the derivatives and original functions in gives

$d/dx(f(x)g(x)) = x^1.7(-sin(x))+1.7x^0.7cos(x)$

Rewriting for simplification and ease of reading gives

$d/dx(f(x)g(x)) = 1.7x^0.7cos(x)-x^1.7sin(x)$

How do you differentiate x^1.7cosxx^1.7cosx?