Working with derivatives and tangents
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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 ...
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