What is the derivative of y=x^{-8cos(x)} ?

The derivative of y=x^{-8cos(x)} is x^{-8cos(x)}(8sin(x)ln(x)-(8cos(x))/x)

What is the first derivative of y=x^{-8cos(x)} ?

The first derivative of y=x^{-8cos(x)} is x^{-8cos(x)}(8sin(x)ln(x)-(8cos(x))/x)

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derivative of

y = x^{- 8 c o s (x)}

x^{- 8 c o s (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

Solution steps

\frac{d}{d x} (x^{- 8 c o s (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{- 8 c o s (x)} = e^{(- 8 c o s (x)) l n (x)}

= \frac{d}{d x} (e^{(- 8 c o s (x)) l n (x)})

Apply the chain rule:

e^{(- 8 c o s (x)) l n (x)} \frac{d}{d x} ((- 8 cos (x)) ln (x))

= e^{(- 8 c o s (x)) l n (x)} \frac{d}{d x} ((- 8 cos (x)) ln (x))

\frac{d}{d x} ((- 8 cos (x)) ln (x)) = 8 sin (x) ln (x) - \frac{8 cos ( x )}{x}

= e^{(- 8 c o s (x)) l n (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

Simplify

e^{(- 8 c o s (x)) l n (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x}) : x^{- 8 c o s (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

= x^{- 8 c o s (x)} (8 sin (x) ln (x) - \frac{8 cos ( x )}{x})

y = sin (t) + \frac{1}{6} e^{t}, (π, \frac{1}{6} e^{π})

\frac{d}{d x} y = x^{4} \cdot x^{5}

\int \frac{( x ^{2} + 1 )}{( x - 8 ) ( x - 7 ) ^{2}} d x

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

\frac{\partial}{\partial x} (\frac{1 + x}{x + y})

What is the derivative of y=x^{-8cos(x)} ?
The derivative of y=x^{-8cos(x)} is x^{-8cos(x)}(8sin(x)ln(x)-(8cos(x))/x)
What is the first derivative of y=x^{-8cos(x)} ?
The first derivative of y=x^{-8cos(x)} is x^{-8cos(x)}(8sin(x)ln(x)-(8cos(x))/x)