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Popular >

derivative of 5^{-x^2}

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

e^{(- x^{2}) l n (5)} \frac{d}{d x} ((- x^{2}) ln (5))

= e^{(- x^{2}) l n (5)} \frac{d}{d x} ((- x^{2}) ln (5))

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

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

Simplify

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

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

Popular Examples

integral from 0 to 2pi of sin^2(5x)

\int_{0}^{2 π} sin^{2} (5 x) d x

integral of t/(sqrt(9+t^2))

\int \frac{t}{9 + t ^{2}} d t

(\partial)/(\partial m)(mx+b)

\frac{\partial}{\partial m} (m x + b)

integral of (1-1/x)^2

\int (1 - \frac{1}{x})^{2} d x

sum from n=1 to infinity of (3^n)/(4^n)

n = 1 \sum \infty \frac{3 ^{n}}{4 ^{n}}

Frequently Asked Questions (FAQ)

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