What is the derivative of x^{-6cos(x}) ?

The derivative of x^{-6cos(x}) is x^{-6cos(x)}(6sin(x)ln(x)-(6cos(x))/x)

What is the first derivative of x^{-6cos(x}) ?

The first derivative of x^{-6cos(x}) is x^{-6cos(x)}(6sin(x)ln(x)-(6cos(x))/x)

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\frac{d}{d x} (x^{- 6 c o s (x)})

x^{- 6 c o s (x)} (6 sin (x) ln (x) - \frac{6 cos ( x )}{x})

Solution steps

\frac{d}{d x} (x^{- 6 c o s (x)})

Apply exponent rule:

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

x^{- 6 c o s (x)} = e^{(- 6 c o s (x)) l n (x)}

= \frac{d}{d x} (e^{(- 6 c o s (x)) l n (x)})

Apply the chain rule:

e^{(- 6 c o s (x)) l n (x)} \frac{d}{d x} ((- 6 cos (x)) ln (x))

= e^{(- 6 c o s (x)) l n (x)} \frac{d}{d x} ((- 6 cos (x)) ln (x))

\frac{d}{d x} ((- 6 cos (x)) ln (x)) = 6 sin (x) ln (x) - \frac{6 cos ( x )}{x}

= e^{(- 6 c o s (x)) l n (x)} (6 sin (x) ln (x) - \frac{6 cos ( x )}{x})

Simplify

e^{(- 6 c o s (x)) l n (x)} (6 sin (x) ln (x) - \frac{6 cos ( x )}{x}) : x^{- 6 c o s (x)} (6 sin (x) ln (x) - \frac{6 cos ( x )}{x})

= x^{- 6 c o s (x)} (6 sin (x) ln (x) - \frac{6 cos ( x )}{x})

\frac{\partial}{\partial x} (sin (x - y) + (x - y))

\int e^{\frac{x}{l}} d x

\int (x^{\frac{4}{3}} - 3 x^{\frac{5}{2}}) d x

\int_{0}^{2 π} sin^{2} (x co) s^{2} x

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

What is the derivative of x^{-6cos(x}) ?
The derivative of x^{-6cos(x}) is x^{-6cos(x)}(6sin(x)ln(x)-(6cos(x))/x)
What is the first derivative of x^{-6cos(x}) ?
The first derivative of x^{-6cos(x}) is x^{-6cos(x)}(6sin(x)ln(x)-(6cos(x))/x)