What is (\partial)/(\partial x)(10^{sqrt(x)}) ?

The answer to (\partial)/(\partial x)(10^{sqrt(x)}) is (ln(10)*5^{sqrt(x)}*2^{sqrt(x)-1})/(sqrt(x))

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(\partial)/(\partial x)(10^{sqrt(x)})

\frac{\partial}{\partial x} (1 0^{x})

\frac{ln ( 10 ) \cdot 5 ^{x} \cdot 2 ^{x - 1}}{x}

Solution steps

\frac{\partial}{\partial x} (1 0^{x})

Apply exponent rule:

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

1 0^{x} = e^{x l n (10)}

= \frac{\partial}{\partial x} (e^{x l n (10)})

Apply the chain rule:

e^{x l n (10)} \frac{\partial}{\partial x} (x ln (10))

= e^{x l n (10)} \frac{\partial}{\partial x} (x ln (10))

\frac{\partial}{\partial x} (x ln (10)) = \frac{ln ( 10 )}{2 x}

= e^{x l n (10)} \frac{ln ( 10 )}{2 x}

Simplify

e^{x l n (10)} \frac{ln ( 10 )}{2 x} : \frac{ln ( 10 ) \cdot 5 ^{x} \cdot 2 ^{x - 1}}{x}

= \frac{ln ( 10 ) \cdot 5 ^{x} \cdot 2 ^{x - 1}}{x}

\frac{x ^{2} - 2 x + 3}{x + 1}

\int \frac{1}{7} d x

\int sin (2 x) ln (sin (2 x)) d x

\frac{10}{s ( s ^{2} + 2 s + 10 )}

\frac{\partial}{\partial y} (x y + y^{2} + y)

What is (\partial)/(\partial x)(10^{sqrt(x)}) ?
The answer to (\partial)/(\partial x)(10^{sqrt(x)}) is (ln(10)*5^{sqrt(x)}*2^{sqrt(x)-1})/(sqrt(x))