What is the derivative of 10^{sqrt(x)} ?

The derivative of 10^{sqrt(x)} is (ln(10)*5^{sqrt(x)}*2^{sqrt(x)-1})/(sqrt(x))

What is the first derivative of 10^{sqrt(x)} ?

The first derivative of 10^{sqrt(x)} is (ln(10)*5^{sqrt(x)}*2^{sqrt(x)-1})/(sqrt(x))

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derivative of

1 0^{x}

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d 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}

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\frac{d}{d x} (\frac{cos ( x )}{2 + sin ( x )})

\frac{d y}{d x} = e^{4 x + 2 y}

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

What is the derivative of 10^{sqrt(x)} ?
The derivative of 10^{sqrt(x)} is (ln(10)*5^{sqrt(x)}*2^{sqrt(x)-1})/(sqrt(x))
What is the first derivative of 10^{sqrt(x)} ?
The first derivative of 10^{sqrt(x)} is (ln(10)*5^{sqrt(x)}*2^{sqrt(x)-1})/(sqrt(x))