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Popular >

derivative of 6^{x^3}

Solution

derivative of

6^{x^{3}}

Solution

ln (6) \cdot 2^{x^{3}} \cdot 3^{x^{3} + 1} x^{2}

Solution steps

\frac{d}{d x} (6^{x^{3}})

Apply exponent rule:

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

6^{x^{3}} = e^{x^{3} l n (6)}

= \frac{d}{d x} (e^{x^{3} l n (6)})

Apply the chain rule:

e^{x^{3} l n (6)} \frac{d}{d x} (x^{3} ln (6))

= e^{x^{3} l n (6)} \frac{d}{d x} (x^{3} ln (6))

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

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

Simplify

e^{x^{3} l n (6)} \cdot 3 ln (6) x^{2} : ln (6) \cdot 2^{x^{3}} \cdot 3^{x^{3} + 1} x^{2}

= ln (6) \cdot 2^{x^{3}} \cdot 3^{x^{3} + 1} x^{2}

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Frequently Asked Questions (FAQ)

What is the derivative of 6^{x^3} ?
The derivative of 6^{x^3} is ln(6)*2^{x^3}*3^{x^3+1}x^2
What is the first derivative of 6^{x^3} ?
The first derivative of 6^{x^3} is ln(6)*2^{x^3}*3^{x^3+1}x^2