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Popular >

derivative of 5^{-2x}

Solution

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

Solution

- 2 ln (5) \cdot 2 5^{- x}

Solution steps

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

Simplify

5^{- 2 x} : 2 5^{- x}

= \frac{d}{d x} (2 5^{- x})

Apply exponent rule:

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

2 5^{- x} = e^{(- x) l n (25)}

= \frac{d}{d x} (e^{(- x) l n (25)})

Apply the chain rule:

e^{(- x) l n (25)} \frac{d}{d x} ((- x) ln (25))

= e^{(- x) l n (25)} \frac{d}{d x} ((- x) ln (25))

\frac{d}{d x} ((- x) ln (25)) = - 2 ln (5)

= e^{(- x) l n (25)} (- 2 ln (5))

Simplify

e^{(- x) l n (25)} (- 2 ln (5)) : - 2 ln (5) \cdot 2 5^{- x}

= - 2 ln (5) \cdot 2 5^{- x}

Popular Examples

(d^2)/(dx^2)((e^x)/(cos(x)))

\frac{d ^{2}}{d x ^{2}} (\frac{e ^{x}}{cos ( x )})

(\partial)/(\partial y)(xz+xyz)

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

slope of (-2,-5),(-3,5)slope

(- 2, - 5), (- 3, 5)

integral of (x-sqrt(25-x^2))

\int (x - 25 - x^{2}) d x

limit as x approaches 0 of ln(tan(x))

x \to 0 lim (ln (tan (x)))

Frequently Asked Questions (FAQ)

What is the derivative of 5^{-2x} ?
The derivative of 5^{-2x} is -2ln(5)*25^{-x}
What is the first derivative of 5^{-2x} ?
The first derivative of 5^{-2x} is -2ln(5)*25^{-x}