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

The derivative of a^{5x} is 5a^{5x}ln(a)

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

The first derivative of a^{5x} is 5a^{5x}ln(a)

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

5 a^{5 x} ln (a)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x ln (a)) = 5 ln (a)

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

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

= 5 a^{5 x} ln (a)

f (x) = x^{3} + 4 x - 4, (1, 1)

\int_{0}^{0.5} (1 - x^{2})^{0.5} d x

\int \frac{1}{a x} d x

\frac{d}{d x} (z + y^{3} + y + x)

x \to - 2 lim (x^{2} - 4 x + 10)

What is the derivative of a^{5x} ?
The derivative of a^{5x} is 5a^{5x}ln(a)
What is the first derivative of a^{5x} ?
The first derivative of a^{5x} is 5a^{5x}ln(a)