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Popular Calculus >

derivative of y=x^4-3x^{-2}+1

Solution

derivative of

y = x^{4} - 3 x^{- 2} + 1

Solution

4 x^{3} + \frac{6}{x ^{3}}

Solution steps

\frac{d}{d x} (x^{4} - 3 x^{- 2} + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (3 x^{- 2}) + \frac{d}{d x} (1)

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

\frac{d}{d x} (1) = 0

= 4 x^{3} - (- \frac{6}{x ^{3}}) + 0

Simplify

= 4 x^{3} + \frac{6}{x ^{3}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=x^4-3x^{-2}+1 ?
The derivative of y=x^4-3x^{-2}+1 is 4x^3+6/(x^3)
What is the first derivative of y=x^4-3x^{-2}+1 ?
The first derivative of y=x^4-3x^{-2}+1 is 4x^3+6/(x^3)