What is the derivative of f(x)=12x^4+3x^3+5x^{-2}-4 ?

The derivative of f(x)=12x^4+3x^3+5x^{-2}-4 is 48x^3+9x^2-(10)/(x^3)

What is the first derivative of f(x)=12x^4+3x^3+5x^{-2}-4 ?

The first derivative of f(x)=12x^4+3x^3+5x^{-2}-4 is 48x^3+9x^2-(10)/(x^3)

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derivative of

f (x) = 12 x^{4} + 3 x^{3} + 5 x^{- 2} - 4

48 x^{3} + 9 x^{2} - \frac{10}{x ^{3}}

Solution steps

\frac{d}{d x} (12 x^{4} + 3 x^{3} + 5 x^{- 2} - 4)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (12 x^{4}) + \frac{d}{d x} (3 x^{3}) + \frac{d}{d x} (5 x^{- 2}) - \frac{d}{d x} (4)

\frac{d}{d x} (12 x^{4}) = 48 x^{3}

\frac{d}{d x} (3 x^{3}) = 9 x^{2}

\frac{d}{d x} (5 x^{- 2}) = - \frac{10}{x ^{3}}

\frac{d}{d x} (4) = 0

= 48 x^{3} + 9 x^{2} - \frac{10}{x ^{3}} - 0

Simplify

= 48 x^{3} + 9 x^{2} - \frac{10}{x ^{3}}

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What is the derivative of f(x)=12x^4+3x^3+5x^{-2}-4 ?
The derivative of f(x)=12x^4+3x^3+5x^{-2}-4 is 48x^3+9x^2-(10)/(x^3)
What is the first derivative of f(x)=12x^4+3x^3+5x^{-2}-4 ?
The first derivative of f(x)=12x^4+3x^3+5x^{-2}-4 is 48x^3+9x^2-(10)/(x^3)