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Popular >

derivative of (5x^3^x)

Solution

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

Solution

(ln (5 x^{3}) + 3) (5 x^{3})^{x}

Solution steps

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

Apply exponent rule:

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

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

= \frac{d}{d x} (e^{x l n (5 x^{3})})

Apply the chain rule:

e^{x l n (5 x^{3})} \frac{d}{d x} (x ln (5 x^{3}))

= e^{x l n (5 x^{3})} \frac{d}{d x} (x ln (5 x^{3}))

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

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

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

= (ln (5 x^{3}) + 3) (5 x^{3})^{x}

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\frac{d y}{d x} = \frac{3 y}{2 x}

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derivative of (4x^2-3(4x^2+3))

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Frequently Asked Questions (FAQ)

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