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

The derivative of 5^{-4x} is -4ln(5)*625^{-x}

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

The first derivative of 5^{-4x} is -4ln(5)*625^{-x}

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

- 4 ln (5) \cdot 62 5^{- x}

Solution steps

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

Simplify

5^{- 4 x} : 62 5^{- x}

= \frac{d}{d x} (62 5^{- x})

Apply exponent rule:

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

62 5^{- x} = e^{(- x) l n (625)}

= \frac{d}{d x} (e^{(- x) l n (625)})

Apply the chain rule:

e^{(- x) l n (625)} \frac{d}{d x} ((- x) ln (625))

= e^{(- x) l n (625)} \frac{d}{d x} ((- x) ln (625))

\frac{d}{d x} ((- x) ln (625)) = - 4 ln (5)

= e^{(- x) l n (625)} (- 4 ln (5))

Simplify

e^{(- x) l n (625)} (- 4 ln (5)) : - 4 ln (5) \cdot 62 5^{- x}

= - 4 ln (5) \cdot 62 5^{- x}

x \to 0 lim (e^{5 x})

\int_{0}^{\frac{π}{3}} 3 sec^{2} (x) d x

4 x + y^{2} = 9, x = 2 y

\frac{\partial}{\partial y} (e^{x} cos (y) + yz)

30 x - 3 x

What is the derivative of 5^{-4x} ?
The derivative of 5^{-4x} is -4ln(5)*625^{-x}
What is the first derivative of 5^{-4x} ?
The first derivative of 5^{-4x} is -4ln(5)*625^{-x}