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Popular >

derivative of (4x^x)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

Popular Examples

integral of 10x^4-2sec^2(x)

\int 10 x^{4} - 2 sec^{2} (x) d x

tangent of 4/(x^2)tangent of

\frac{4}{x ^{2}}

tangent of 9/x tangent of

\frac{9}{x}

slope of x^2+xy-(y^2)/4 =1 slope

x^{2} + x y - \frac{y ^{2}}{4} = 1

derivative of f(x)=(5x+2x^2)^2 derivative of

f (x) = (5 x + 2 x^{2})^{2}

Frequently Asked Questions (FAQ)

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