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

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

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

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

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derivative of

f (x) = 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}

\frac{d}{d x} (\frac{2 x}{x ^{2} + 4})

\int \frac{x ^{2} - 6 x + 9}{x ^{2} - 6 x + 45} d x

y^{^{'}} = (3 x - 2)^{2} (5 x + 4)

t^{3} - 12 t

y^{^{''}} = \frac{1}{x ^{2}} y

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