What is the derivative of 10^{2sqrt(x)} ?

The derivative of 10^{2sqrt(x)} is (ln(10)*100^{sqrt(x)})/(sqrt(x))

What is the first derivative of 10^{2sqrt(x)} ?

The first derivative of 10^{2sqrt(x)} is (ln(10)*100^{sqrt(x)})/(sqrt(x))

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derivative of

1 0^{2 x}

\frac{ln ( 10 ) \cdot 10 0 ^{x}}{x}

Solution steps

\frac{d}{d x} (1 0^{2 x})

Simplify

1 0^{2 x} : 10 0^{x}

= \frac{d}{d x} (10 0^{x})

Apply exponent rule:

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

10 0^{x} = e^{x l n (100)}

= \frac{d}{d x} (e^{x l n (100)})

Apply the chain rule:

e^{x l n (100)} \frac{d}{d x} (x ln (100))

= e^{x l n (100)} \frac{d}{d x} (x ln (100))

\frac{d}{d x} (x ln (100)) = \frac{ln ( 10 )}{x}

= e^{x l n (100)} \frac{ln ( 10 )}{x}

Simplify

e^{x l n (100)} \frac{ln ( 10 )}{x} : \frac{ln ( 10 ) \cdot 10 0 ^{x}}{x}

= \frac{ln ( 10 ) \cdot 10 0 ^{x}}{x}

\int 6 + 6 tan^{2} (x) d x

\int - 7 d x

\int_{0}^{1} \frac{x ^{2}}{x ^{3} - 5} d x

\int \frac{x ^{3}}{x ^{2} + 121} d x

f (x) = \frac{1}{x ^{2} - 5}

What is the derivative of 10^{2sqrt(x)} ?
The derivative of 10^{2sqrt(x)} is (ln(10)*100^{sqrt(x)})/(sqrt(x))
What is the first derivative of 10^{2sqrt(x)} ?
The first derivative of 10^{2sqrt(x)} is (ln(10)*100^{sqrt(x)})/(sqrt(x))