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Popular >

derivative of 5^{sqrt(x)}

Solution

derivative of

5^{x}

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of sqrt(3x-4)

\int 3 x - 4 d x

limit as x approaches-1 of (x-2)/(x^2-1)

x \to - 1 lim (\frac{x - 2}{x ^{2} - 1})

integral of 1/(u^2+1)

\int \frac{1}{u ^{2} + 1} d u

(dy)/(dx)= 1/(sqrt(x))

\frac{d y}{d x} = \frac{1}{x}

integral from 0 to 1 of (e^{x^2})

\int_{0}^{1} (e^{x^{2}}) d x

Frequently Asked Questions (FAQ)

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