What is the derivative of-1/5 x^5+2x^3-72x-4 ?

The derivative of-1/5 x^5+2x^3-72x-4 is -x^4+6x^2-72

What is the first derivative of-1/5 x^5+2x^3-72x-4 ?

The first derivative of-1/5 x^5+2x^3-72x-4 is -x^4+6x^2-72

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\frac{d}{d x} (- \frac{1}{5} x^{5} + 2 x^{3} - 72 x - 4)

- x^{4} + 6 x^{2} - 72

Solution steps

\frac{d}{d x} (- \frac{1}{5} x^{5} + 2 x^{3} - 72 x - 4)

Simplify

- \frac{1}{5} x^{5} + 2 x^{3} - 72 x - 4 : - \frac{x ^{5}}{5} + 2 x^{3} - 72 x - 4

= \frac{d}{d x} (- \frac{x ^{5}}{5} + 2 x^{3} - 72 x - 4)

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (\frac{x ^{5}}{5}) + \frac{d}{d x} (2 x^{3}) - \frac{d}{d x} (72 x) - \frac{d}{d x} (4)

\frac{d}{d x} (\frac{x ^{5}}{5}) = x^{4}

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

\frac{d}{d x} (72 x) = 72

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

= - x^{4} + 6 x^{2} - 72 - 0

Simplify

= - x^{4} + 6 x^{2} - 72

\int \frac{1 + x ^{2}}{x} d x

\int \frac{1}{5 x ( 6 + x )} d x

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

\int 3 x sin^{2} (x^{2}) d x

- 4 cos (x)

What is the derivative of-1/5 x^5+2x^3-72x-4 ?
The derivative of-1/5 x^5+2x^3-72x-4 is -x^4+6x^2-72
What is the first derivative of-1/5 x^5+2x^3-72x-4 ?
The first derivative of-1/5 x^5+2x^3-72x-4 is -x^4+6x^2-72