What is the derivative of y=x^{7x} ?

The derivative of y=x^{7x} is 7x^{7x}(ln(x)+1)

What is the first derivative of y=x^{7x} ?

The first derivative of y=x^{7x} is 7x^{7x}(ln(x)+1)

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derivative of

y = x^{7 x}

7 x^{7 x} (ln (x) + 1)

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) + 1)

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

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

= 7 x^{7 x} (ln (x) + 1)

e^{- 2 x}, 2

\frac{d y}{d x} = \frac{x}{y}, y (0) = - 3

\int \frac{1}{2 x ^{2} - 5} d x

\frac{e ^{x}}{e ^{x} + 7}

\frac{s e ^{- 3 s}}{( s - 4 ) ^{3}}

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