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Popular >

derivative of e^{sqrt(ln(x^2)})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (x^{2})) = \frac{1}{x ln ( x ^{2} )}

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

Simplify

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

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

Popular Examples

derivative of sqrt(-x^2+4)

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

derivative of 4^x-2^x derivative of

4^{x} - 2^{x}

(\partial)/(\partial x)(2x^2+9y^2+3)

\frac{\partial}{\partial x} (2 x^{2} + 9 y^{2} + 3)

derivative of |2x^3+4x-2|

\frac{d}{d x} (2 x^{3} + 4 x - 2)

derivative of 4x^3-16x derivative of

4 x^{3} - 16 x

Frequently Asked Questions (FAQ)

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