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Popular >

derivative of y=x^{6x}

Solution

derivative of

y = x^{6 x}

Solution

6 x^{6 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{6 x})

Apply exponent rule:

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

x^{6 x} = e^{6 x l n (x)}

= \frac{d}{d x} (e^{6 x l n (x)})

Apply the chain rule:

e^{6 x l n (x)} \frac{d}{d x} (6 x ln (x))

= e^{6 x l n (x)} \frac{d}{d x} (6 x ln (x))

\frac{d}{d x} (6 x ln (x)) = 6 (ln (x) + 1)

= e^{6 x l n (x)} \cdot 6 (ln (x) + 1)

e^{6 x l n (x)} = x^{6 x}

= 6 x^{6 x} (ln (x) + 1)

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x \to 0 lim (∣ x ∣^{∣ x ∣})

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\int \frac{- x ^{3} + 2 x ^{2} - x + 1}{x ( x ^{2} + 1 ) ^{2}} d x

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\int (x - 7) sin (π x) d x

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((x^{3} - 16 x)^{12}), at x = - 4

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\int 8 sin (2) (x) cos (3) (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of y=x^{6x} ?
The derivative of y=x^{6x} is 6x^{6x}(ln(x)+1)
What is the first derivative of y=x^{6x} ?
The first derivative of y=x^{6x} is 6x^{6x}(ln(x)+1)