How do you find the derivative of #h(x) = cos(4x^3)#?

1 Answer
Stefan V.
Aug 14, 2015

#h^' = -12x^2 * sin(4x^3)#

Explanation:

You can differentiate this function by using the chain rule for #cosu#, with #u = 4x^3#.

You need to know that

#d/dx(cosx) = - sinx#

So, the derivative of #h(x)# will be

#d/dx(cosu) = [d/(du)cosu] * d/dx(u)#

#d/dx(cosu) = -sinu * d/dx(4x^3)#

#d/dx(cos(4x^3)) = - sin(4x^3) * 12x^2#

#d/dx(cos(4x^3)) = color(green)(-12x^2 * sin(4x^3))#

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