What is the derivative of 5/((2x^3)+2cos(x)) ?

The derivative of 5/((2x^3)+2cos(x)) is -(15)/(8x^4)-2sin(x)

What is the first derivative of 5/((2x^3)+2cos(x)) ?

The first derivative of 5/((2x^3)+2cos(x)) is -(15)/(8x^4)-2sin(x)

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\frac{d}{d x} (\frac{5}{( 2 x ) ^{3}} + 2 cos (x))

- \frac{15}{8 x ^{4}} - 2 sin (x)

Solution steps

\frac{d}{d x} (\frac{5}{( 2 x ) ^{3}} + 2 cos (x))

Simplify

\frac{5}{( 2 x ) ^{3}} + 2 cos (x) : \frac{5}{8 x ^{3}} + 2 cos (x)

= \frac{d}{d x} (\frac{5}{8 x ^{3}} + 2 cos (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{5}{8 x ^{3}}) + \frac{d}{d x} (2 cos (x))

\frac{d}{d x} (\frac{5}{8 x ^{3}}) = - \frac{15}{8 x ^{4}}

\frac{d}{d x} (2 cos (x)) = - 2 sin (x)

= - \frac{15}{8 x ^{4}} - 2 sin (x)

What is the derivative of 5/((2x^3)+2cos(x)) ?
The derivative of 5/((2x^3)+2cos(x)) is -(15)/(8x^4)-2sin(x)
What is the first derivative of 5/((2x^3)+2cos(x)) ?
The first derivative of 5/((2x^3)+2cos(x)) is -(15)/(8x^4)-2sin(x)