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Popular >

derivative of y=sqrt(x)^{3x}

Solution

derivative of

y = x^{3 x}

Solution

3 (x)^{3 x} (ln (x) + \frac{1}{2})

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x ln (x)) = 3 (ln (x) + \frac{1}{2})

= e^{3 x l n (x)} \cdot 3 (ln (x) + \frac{1}{2})

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

= 3 (x)^{3 x} (ln (x) + \frac{1}{2})

Popular Examples

y^{''}+y=sec(t)

y^{^{''}} + y = sec (t)

sum from n=1 to infinity of (6n)/(9-2n)

n = 1 \sum \infty \frac{6 n}{9 - 2 n}

maclaurin f(x)=(1+x)^{-5/3}maclaurin

f (x) = (1 + x)^{- \frac{5}{3}}

integral of x^2(6x^3-5)^4

\int x^{2} (6 x^{3} - 5)^{4} d x

limit as x approaches 0 of (3^x)/(3^x-1)

x \to 0 lim (\frac{3 ^{x}}{3 ^{x} - 1})

Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(x)^{3x} ?
The derivative of y=sqrt(x)^{3x} is 3(sqrt(x))^{3x}(ln(sqrt(x))+1/2)
What is the first derivative of y=sqrt(x)^{3x} ?
The first derivative of y=sqrt(x)^{3x} is 3(sqrt(x))^{3x}(ln(sqrt(x))+1/2)