What is the derivative of 5^{2x^3} ?

The derivative of 5^{2x^3} is e^{x^3ln(25)}*6ln(5)x^2

What is the first derivative of 5^{2x^3} ?

The first derivative of 5^{2x^3} is e^{x^3ln(25)}*6ln(5)x^2

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\frac{d}{d x} (5^{2 x^{3}})

e^{x^{3} l n (25)} \cdot 6 ln (5) x^{2}

Solution steps

\frac{d}{d x} (5^{2 x^{3}})

Simplify

5^{2 x^{3}} : 2 5^{x^{3}}

= \frac{d}{d x} (2 5^{x^{3}})

Apply exponent rule:

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

2 5^{x^{3}} = e^{x^{3} l n (25)}

= \frac{d}{d x} (e^{x^{3} l n (25)})

Apply the chain rule:

e^{x^{3} l n (25)} \frac{d}{d x} (x^{3} ln (25))

= e^{x^{3} l n (25)} \frac{d}{d x} (x^{3} ln (25))

\frac{d}{d x} (x^{3} ln (25)) = 6 ln (5) x^{2}

= e^{x^{3} l n (25)} \cdot 6 ln (5) x^{2}

What is the derivative of 5^{2x^3} ?
The derivative of 5^{2x^3} is e^{x^3ln(25)}*6ln(5)x^2
What is the first derivative of 5^{2x^3} ?
The first derivative of 5^{2x^3} is e^{x^3ln(25)}*6ln(5)x^2