Computing Derivatives

Problem : Compute the derivative of

g(x) =

Problem : Find the derivative of

h(x) = e ^x²+sin(x)

Problem : Find the derivative of g(x) = log(x) , noting that g has inverse f (x) = e ^x and using implicit differentiation.

We differentiate both sides of f (g(x)) = x with respect to x to obtain

f'(g(x))g'(x) = 1

g'(x) =

In our case, this implies

g'(x) =

Figure %: Plot of g(x) = log(x) and g'(x) =

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h'(x)	=	f'(g(x))g'(x)
	=	(e ^x²+sin(x))(2x + cos(x))