What is the derivative of 7^{sqrt(x)} ?

The derivative of 7^{sqrt(x)} is (ln(7)*7^{sqrt(x)})/(2sqrt(x))

What is the first derivative of 7^{sqrt(x)} ?

The first derivative of 7^{sqrt(x)} is (ln(7)*7^{sqrt(x)})/(2sqrt(x))

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\frac{d}{d x} (7^{x})

\frac{ln ( 7 ) \cdot 7 ^{x}}{2 x}

Solution steps

\frac{d}{d x} (7^{x})

Apply exponent rule:

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

7^{x} = e^{x l n (7)}

= \frac{d}{d x} (e^{x l n (7)})

Apply the chain rule:

e^{x l n (7)} \frac{d}{d x} (x ln (7))

= e^{x l n (7)} \frac{d}{d x} (x ln (7))

\frac{d}{d x} (x ln (7)) = \frac{ln ( 7 )}{2 x}

= e^{x l n (7)} \frac{ln ( 7 )}{2 x}

Simplify

e^{x l n (7)} \frac{ln ( 7 )}{2 x} : \frac{ln ( 7 ) \cdot 7 ^{x}}{2 x}

= \frac{ln ( 7 ) \cdot 7 ^{x}}{2 x}

What is the derivative of 7^{sqrt(x)} ?
The derivative of 7^{sqrt(x)} is (ln(7)*7^{sqrt(x)})/(2sqrt(x))
What is the first derivative of 7^{sqrt(x)} ?
The first derivative of 7^{sqrt(x)} is (ln(7)*7^{sqrt(x)})/(2sqrt(x))