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}}

\int_{1200}^{1210} 0.1 x^{2} d x

(\frac{x ^{2} + 1}{x ^{2} - 1})^{7}

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

n = 0 \sum \infty \frac{1}{3 ^{n}}

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)