What is the derivative of f(x)=5^{sqrt(x)} ?

The derivative of f(x)=5^{sqrt(x)} is (ln(5)*5^{sqrt(x)})/(2sqrt(x))

What is the first derivative of f(x)=5^{sqrt(x)} ?

The first derivative of f(x)=5^{sqrt(x)} is (ln(5)*5^{sqrt(x)})/(2sqrt(x))

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derivative of

f (x) = 5^{x}

\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}

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

y^{^{'}} - x y = x y^{\frac{3}{2}}

\frac{1}{x}

y = 9 arctan (x - 1 + x^{2})

\int \frac{x}{x - 5} d x

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