What is the derivative of f(x)=x^{5x} ?

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

What is the first derivative of f(x)=x^{5x} ?

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

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derivative of

f (x) = 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)

y = x^{4} + 9 e^{x}, (0, 9)

2 y d x + (y - 2 x) d y = 0

y = (3 x^{2}) (5 x^{4})

\frac{d y}{d x} = - x^{\frac{1}{3}}

\int \frac{y ^{2} - 64}{y} d y

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