What is the derivative of 3x^{5x} ?

The derivative of 3x^{5x} is 15x^{5x}(ln(x)+1)

What is the first derivative of 3x^{5x} ?

The first derivative of 3x^{5x} is 15x^{5x}(ln(x)+1)

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\frac{d}{d x} (3 x^{5 x})

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

Solution steps

\frac{d}{d x} (3 x^{5 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \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)}

= 3 \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)

= 3 e^{5 x l n (x)} \cdot 5 (ln (x) + 1)

Simplify

3 e^{5 x l n (x)} \cdot 5 (ln (x) + 1) : 15 x^{5 x} (ln (x) + 1)

= 15 x^{5 x} (ln (x) + 1)

\int x e^{7 x} d x

x^{2} + y^{2} = 25, y = 0

\int_{0}^{2} 3^{x} d x

arctan (2 x)

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

What is the derivative of 3x^{5x} ?
The derivative of 3x^{5x} is 15x^{5x}(ln(x)+1)
What is the first derivative of 3x^{5x} ?
The first derivative of 3x^{5x} is 15x^{5x}(ln(x)+1)