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Popular >

derivative of 4x^{2x}

Solution

\frac{d}{d x} (4 x^{2 x})

Solution

8 x^{2 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (4 x^{2 x})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{2 x})

Apply exponent rule:

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

x^{2 x} = e^{2 x l n (x)}

= 4 \frac{d}{d x} (e^{2 x l n (x)})

Apply the chain rule:

e^{2 x l n (x)} \frac{d}{d x} (2 x ln (x))

= e^{2 x l n (x)} \frac{d}{d x} (2 x ln (x))

\frac{d}{d x} (2 x ln (x)) = 2 (ln (x) + 1)

= 4 e^{2 x l n (x)} \cdot 2 (ln (x) + 1)

Simplify

4 e^{2 x l n (x)} \cdot 2 (ln (x) + 1) : 8 x^{2 x} (ln (x) + 1)

= 8 x^{2 x} (ln (x) + 1)

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Frequently Asked Questions (FAQ)

What is the derivative of 4x^{2x} ?
The derivative of 4x^{2x} is 8x^{2x}(ln(x)+1)
What is the first derivative of 4x^{2x} ?
The first derivative of 4x^{2x} is 8x^{2x}(ln(x)+1)