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Popular >

derivative of x^{2ax}

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

Popular Examples

derivative of f(b)= b/(z+n)derivative of

f (b) = \frac{b}{z + n}

integral of ((6x^2+5x+6))/((x^2+1)^2)

\int \frac{( 6 x ^{2} + 5 x + 6 )}{( x ^{2} + 1 ) ^{2}} d x

\frac{d S}{d r} = k S

integral of sin^3(u)

\int sin^{3} (u) d u

derivative of (ln(x)^{-1})

\frac{d}{d x} ((ln (x))^{- 1})

Frequently Asked Questions (FAQ)

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