What is the derivative of x^{-3x} ?

The derivative of x^{-3x} is x^{-3x}(-3ln(x)-3)

What is the first derivative of x^{-3x} ?

The first derivative of x^{-3x} is x^{-3x}(-3ln(x)-3)

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\frac{d}{d x} (x^{- 3 x})

x^{- 3 x} (- 3 ln (x) - 3)

Solution steps

\frac{d}{d x} (x^{- 3 x})

Apply exponent rule:

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

x^{- 3 x} = e^{(- 3 x) l n (x)}

= \frac{d}{d x} (e^{(- 3 x) l n (x)})

Apply the chain rule:

e^{(- 3 x) l n (x)} \frac{d}{d x} ((- 3 x) ln (x))

= e^{(- 3 x) l n (x)} \frac{d}{d x} ((- 3 x) ln (x))

\frac{d}{d x} ((- 3 x) ln (x)) = - 3 ln (x) - 3

= e^{(- 3 x) l n (x)} (- 3 ln (x) - 3)

Simplify

e^{(- 3 x) l n (x)} (- 3 ln (x) - 3) : x^{- 3 x} (- 3 ln (x) - 3)

= x^{- 3 x} (- 3 ln (x) - 3)

\frac{d}{d x} (csch (x))

(3 3 x)^{^{'}}

f (x) = e^{x} cos (x)

\frac{\partial}{\partial z} (\frac{( 7 x + 7 y )}{z})

\frac{d}{d x} (- 9 x)

What is the derivative of x^{-3x} ?
The derivative of x^{-3x} is x^{-3x}(-3ln(x)-3)
What is the first derivative of x^{-3x} ?
The first derivative of x^{-3x} is x^{-3x}(-3ln(x)-3)