What is the derivative of 656112^{sqrt(x)} ?

The derivative of 656112^{sqrt(x)} is (ln(656112)*41007^{sqrt(x)}*2^{4sqrt(x)-1})/(sqrt(x))

What is the first derivative of 656112^{sqrt(x)} ?

The first derivative of 656112^{sqrt(x)} is (ln(656112)*41007^{sqrt(x)}*2^{4sqrt(x)-1})/(sqrt(x))

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\frac{d}{d x} (65611 2^{x})

\frac{ln ( 656112 ) \cdot 4100 7 ^{x} \cdot 2 ^{4 x - 1}}{x}

Solution steps

\frac{d}{d x} (65611 2^{x})

Apply exponent rule:

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

65611 2^{x} = e^{x l n (656112)}

= \frac{d}{d x} (e^{x l n (656112)})

Apply the chain rule:

e^{x l n (656112)} \frac{d}{d x} (x ln (656112))

= e^{x l n (656112)} \frac{d}{d x} (x ln (656112))

\frac{d}{d x} (x ln (656112)) = \frac{ln ( 656112 )}{2 x}

= e^{x l n (656112)} \frac{ln ( 656112 )}{2 x}

Simplify

e^{x l n (656112)} \frac{ln ( 656112 )}{2 x} : \frac{ln ( 656112 ) \cdot 4100 7 ^{x} \cdot 2 ^{4 x - 1}}{x}

= \frac{ln ( 656112 ) \cdot 4100 7 ^{x} \cdot 2 ^{4 x - 1}}{x}

\int \frac{1}{sin ( 2 x )} d x

\frac{d}{d x} (3 sec (8 x))

9 e x cos (x)

\int \frac{x ^{4}}{5 x ^{5} + 4} d x

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

What is the derivative of 656112^{sqrt(x)} ?
The derivative of 656112^{sqrt(x)} is (ln(656112)*41007^{sqrt(x)}*2^{4sqrt(x)-1})/(sqrt(x))
What is the first derivative of 656112^{sqrt(x)} ?
The first derivative of 656112^{sqrt(x)} is (ln(656112)*41007^{sqrt(x)}*2^{4sqrt(x)-1})/(sqrt(x))