What is the derivative of (x^2+2^{-5}cos(x)) ?

The derivative of (x^2+2^{-5}cos(x)) is -(10xcos(x))/((x^2+2)^6)-(sin(x))/((x^2+2)^5)

What is the first derivative of (x^2+2^{-5}cos(x)) ?

The first derivative of (x^2+2^{-5}cos(x)) is -(10xcos(x))/((x^2+2)^6)-(sin(x))/((x^2+2)^5)

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

- \frac{10 x cos ( x )}{( x ^{2} + 2 ) ^{6}} - \frac{sin ( x )}{( x ^{2} + 2 ) ^{5}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (x^{2} + 2)^{- 5}, g = cos (x)

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

\frac{d}{d x} ((x^{2} + 2)^{- 5}) = - \frac{10 x}{( x ^{2} + 2 ) ^{6}}

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

= (- \frac{10 x}{( x ^{2} + 2 ) ^{6}}) cos (x) + (- sin (x)) (x^{2} + 2)^{- 5}

Simplify

(- \frac{10 x}{( x ^{2} + 2 ) ^{6}}) cos (x) + (- sin (x)) (x^{2} + 2)^{- 5} : - \frac{10 x cos ( x )}{( x ^{2} + 2 ) ^{6}} - \frac{sin ( x )}{( x ^{2} + 2 ) ^{5}}

= - \frac{10 x cos ( x )}{( x ^{2} + 2 ) ^{6}} - \frac{sin ( x )}{( x ^{2} + 2 ) ^{5}}

\frac{d}{d x} (x^{5} - 5 x^{3} - 20 x - 2)

y = x^{2}, (0, 2)

\int cos (x) x^{2} d x

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

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

What is the derivative of (x^2+2^{-5}cos(x)) ?
The derivative of (x^2+2^{-5}cos(x)) is -(10xcos(x))/((x^2+2)^6)-(sin(x))/((x^2+2)^5)
What is the first derivative of (x^2+2^{-5}cos(x)) ?
The first derivative of (x^2+2^{-5}cos(x)) is -(10xcos(x))/((x^2+2)^6)-(sin(x))/((x^2+2)^5)