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Popular >

derivative of (x^2^{2x})

Solution

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

Solution

2 x^{4 x} (2 ln (x) + 2)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

e^{2 x l n (x^{2})} \cdot 2 (ln (x^{2}) + 2) : 2 x^{4 x} (2 ln (x) + 2)

= 2 x^{4 x} (2 ln (x) + 2)

Popular Examples

integral from 0 to pi/6 of 17sec^4(x)

\int_{0}^{\frac{π}{6}} 17 sec^{4} (x) d x

inverse oflaplace (8s^2-4s+12)/(s(s^2+4))inverse laplace

\frac{8 s ^{2} - 4 s + 12}{s ( s ^{2} + 4 )}

tangent of f(x)=sqrt(x),\at x= 49/121 tangent of

f (x) = x, at x = \frac{49}{121}

derivative of 1/(sqrt(2-x))

\frac{d}{d x} (\frac{1}{2 - x})

(d^4)/(dx^4)(2e^{x^2})

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

Frequently Asked Questions (FAQ)

What is the derivative of (x^2^{2x}) ?
The derivative of (x^2^{2x}) is 2x^{4x}(2ln(x)+2)
What is the first derivative of (x^2^{2x}) ?
The first derivative of (x^2^{2x}) is 2x^{4x}(2ln(x)+2)