What is the derivative of 4^{-5x^3} ?

The derivative of 4^{-5x^3} is -15ln(2)*2^{-10x^3+1}x^2

What is the first derivative of 4^{-5x^3} ?

The first derivative of 4^{-5x^3} is -15ln(2)*2^{-10x^3+1}x^2

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

- 15 ln (2) \cdot 2^{- 10 x^{3} + 1} x^{2}

Solution steps

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

Simplify

4^{- 5 x^{3}} : 102 4^{- x^{3}}

= \frac{d}{d x} (102 4^{- x^{3}})

Apply exponent rule:

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

102 4^{- x^{3}} = e^{(- x^{3}) l n (1024)}

= \frac{d}{d x} (e^{(- x^{3}) l n (1024)})

Apply the chain rule:

e^{(- x^{3}) l n (1024)} \frac{d}{d x} ((- x^{3}) ln (1024))

= e^{(- x^{3}) l n (1024)} \frac{d}{d x} ((- x^{3}) ln (1024))

\frac{d}{d x} ((- x^{3}) ln (1024)) = - 30 ln (2) x^{2}

= e^{(- x^{3}) l n (1024)} (- 30 ln (2) x^{2})

Simplify

e^{(- x^{3}) l n (1024)} (- 30 ln (2) x^{2}) : - 15 ln (2) \cdot 2^{- 10 x^{3} + 1} x^{2}

= - 15 ln (2) \cdot 2^{- 10 x^{3} + 1} x^{2}

\frac{\partial}{\partial x} (x + 2 y + 3 z)

\int_{0}^{1} (e^{x}) - (x e^{x}) d x

\int_{0}^{0.6} 10000 x d x

9 x^{3}

(x \cdot x - 1) y^{^{'}} - x y (1 - y) = 0

What is the derivative of 4^{-5x^3} ?
The derivative of 4^{-5x^3} is -15ln(2)*2^{-10x^3+1}x^2
What is the first derivative of 4^{-5x^3} ?
The first derivative of 4^{-5x^3} is -15ln(2)*2^{-10x^3+1}x^2