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Popular >

derivative of 3x^{4x}

Solution

\frac{d}{d x} (3 x^{4 x})

Solution

12 x^{4 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (3 x^{4 x})

Take the constant out:

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

= 3 \frac{d}{d x} (x^{4 x})

Apply exponent rule:

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

x^{4 x} = e^{4 x l n (x)}

= 3 \frac{d}{d x} (e^{4 x l n (x)})

Apply the chain rule:

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

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

\frac{d}{d x} (4 x ln (x)) = 4 (ln (x) + 1)

= 3 e^{4 x l n (x)} \cdot 4 (ln (x) + 1)

Simplify

3 e^{4 x l n (x)} \cdot 4 (ln (x) + 1) : 12 x^{4 x} (ln (x) + 1)

= 12 x^{4 x} (ln (x) + 1)

Popular Examples

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derivative of f(x)=((x^2-1))/((x^2+x+1))derivative of

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limit as x approaches 1-of x/(x+1)

x \to 1 - lim (\frac{x}{x + 1})

Frequently Asked Questions (FAQ)

What is the derivative of 3x^{4x} ?
The derivative of 3x^{4x} is 12x^{4x}(ln(x)+1)
What is the first derivative of 3x^{4x} ?
The first derivative of 3x^{4x} is 12x^{4x}(ln(x)+1)