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

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

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

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

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\frac{d}{d x} (2^{l n (x)})

\frac{ln ( 2 ) \cdot 2 ^{l n (x) - 1}}{x ln ( x )}

Solution steps

\frac{d}{d x} (2^{l n (x)})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{ln ( 2 ) \cdot 2 ^{l n (x) - 1}}{x ln ( x )}

y = cos (a^{4} + x^{4})

(7, 5), (- 4, - 1)

\int_{0}^{\frac{π}{4}} sec^{5} (x) d x

f (x) = 8 x^{3} - x^{π}

\int \frac{x}{- 5 x ^{2} + 2 x + 1} d x

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