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Popular >

derivative of y=x^{x^2}

Solution

derivative of

y = x^{x^{2}}

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

Popular Examples

(\partial)/(\partial x)(-xcos(y))

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\int 3 cos (x) - \frac{1}{x} d x

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\int_{1}^{11} \frac{1}{x - 8} d x

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\int_{- 2}^{2} \frac{10}{x ^{2} - 4 x - 21} d x

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\int (3 sec (x) tan (x) - 5 csc^{2} (x)) d x

Frequently Asked Questions (FAQ)

What is the derivative of y=x^{x^2} ?
The derivative of y=x^{x^2} is x^{x^2}(2xln(x)+x)
What is the first derivative of y=x^{x^2} ?
The first derivative of y=x^{x^2} is x^{x^2}(2xln(x)+x)