What is the derivative of y=x^{5x} ?

The derivative of y=x^{5x} is 5x^{5x}(ln(x)+1)

What is the first derivative of y=x^{5x} ?

The first derivative of y=x^{5x} is 5x^{5x}(ln(x)+1)

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derivative of

y = x^{5 x}

5 x^{5 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{5 x})

Apply exponent rule:

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

x^{5 x} = e^{5 x l n (x)}

= \frac{d}{d x} (e^{5 x l n (x)})

Apply the chain rule:

e^{5 x l n (x)} \frac{d}{d x} (5 x ln (x))

= e^{5 x l n (x)} \frac{d}{d x} (5 x ln (x))

\frac{d}{d x} (5 x ln (x)) = 5 (ln (x) + 1)

= e^{5 x l n (x)} \cdot 5 (ln (x) + 1)

e^{5 x l n (x)} = x^{5 x}

= 5 x^{5 x} (ln (x) + 1)

\int_{- 1}^{1} (3 t - 5) d t

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

\int (3 x + 1) (4 - x) d x

\frac{( x - 2 )}{x + 3}

\frac{d}{d x} (3 x y)

What is the derivative of y=x^{5x} ?
The derivative of y=x^{5x} is 5x^{5x}(ln(x)+1)
What is the first derivative of y=x^{5x} ?
The first derivative of y=x^{5x} is 5x^{5x}(ln(x)+1)