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Popular >

derivative of f(3)= 1/x+(x^2-1)^3

Solution

derivative of

f (3) = \frac{1}{x} + (x^{2} - 1)^{3}

Solution

- \frac{1}{x ^{2}} + 6 x (x^{2} - 1)^{2}

Solution steps

\frac{d}{d x} (\frac{1}{x} + (x^{2} - 1)^{3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{x}) + \frac{d}{d x} ((x^{2} - 1)^{3})

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

\frac{d}{d x} ((x^{2} - 1)^{3}) = 6 x (x^{2} - 1)^{2}

= - \frac{1}{x ^{2}} + 6 x (x^{2} - 1)^{2}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(3)= 1/x+(x^2-1)^3 ?
The derivative of f(3)= 1/x+(x^2-1)^3 is -1/(x^2)+6x(x^2-1)^2
What is the first derivative of f(3)= 1/x+(x^2-1)^3 ?
The first derivative of f(3)= 1/x+(x^2-1)^3 is -1/(x^2)+6x(x^2-1)^2