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Popular >

derivative of y=sqrt(x)^{7x}

Solution

derivative of

y = x^{7 x}

Solution

7 (x)^{7 x} (ln (x) + \frac{1}{2})

Solution steps

\frac{d}{d x} ((x)^{7 x})

Apply exponent rule:

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

(x)^{7 x} = e^{7 x l n (x)}

= \frac{d}{d x} (e^{7 x l n (x)})

Apply the chain rule:

e^{7 x l n (x)} \frac{d}{d x} (7 x ln (x))

= e^{7 x l n (x)} \frac{d}{d x} (7 x ln (x))

\frac{d}{d x} (7 x ln (x)) = 7 (ln (x) + \frac{1}{2})

= e^{7 x l n (x)} \cdot 7 (ln (x) + \frac{1}{2})

e^{7 x l n (x)} = (x)^{7 x}

= 7 (x)^{7 x} (ln (x) + \frac{1}{2})

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t^{3} e^{- 3 t}

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x \to 0 lim (6^{x})

(\partial)/(\partial x)(x^3y^7)

\frac{\partial}{\partial x} (x^{3} y^{7})

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\frac{d}{d x} (x^{3} - 7 x^{2} + 14 x - 6)

Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(x)^{7x} ?
The derivative of y=sqrt(x)^{7x} is 7(sqrt(x))^{7x}(ln(sqrt(x))+1/2)
What is the first derivative of y=sqrt(x)^{7x} ?
The first derivative of y=sqrt(x)^{7x} is 7(sqrt(x))^{7x}(ln(sqrt(x))+1/2)