# Working with derivatives and tangents

1.) Find the derivative of the function:

a.) f(x) = x + 1/x^2

b.) f(x) = (2/3rd root of x) + 3 cos x

2.) Find equation of tangent line to the graph of f at the indicated point:

a.) y = (x^2 + 2x)(x + 1) ; (1,6)

https://brainmass.com/math/derivatives/working-derivatives-tangents-7763

#### Solution Preview

1) y = x + (1/x^2)

dy/dx = 1 + d/dx(x^-2)

= 1 + [-2 * x^-3]

= 1 - (2/x^3) Answer

2)y = [2/x^(1/3)] + 3 Cos(x)

dy/dx = 2*(-1/3)[x^(-1/3)-1] + 3*-Sin(x)

= -(2/3)[1/x^(4/3)] - 3 ...

#### Solution Summary

The solutions shows all mathematical steps to arrive at the final answer. This will enable you to solve similar problems yourself.

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