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Popular >

derivative of y=(sqrt(t))^t

Solution

derivative of

y = (t)^{t}

Solution

(t)^{t} (ln (t) + \frac{1}{2})

Solution steps

\frac{d}{d t} ((t)^{t})

Apply exponent rule:

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

(t)^{t} = e^{t l n (t)}

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

Apply the chain rule:

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

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

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

= e^{t l n (t)} (ln (t) + \frac{1}{2})

e^{t l n (t)} = (t)^{t}

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

Graph

Popular Examples

limit as x approaches 1/3 of (x+3)/(x+4)

x \to \frac{1}{3} lim (\frac{x + 3}{x + 4})

derivative of (x^2dx)

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

limit as x approaches-3 of (x^2+x)/(x+3)

x \to - 3 lim (\frac{x ^{2} + x}{x + 3})

integral of 3y^3e^{xy}

\int 3 y^{3} e^{x y} d x

integral of x^2e^{2x+1}

\int x^{2} e^{2 x + 1} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=(sqrt(t))^t ?
The derivative of y=(sqrt(t))^t is (sqrt(t))^t(ln(sqrt(t))+1/2)
What is the first derivative of y=(sqrt(t))^t ?
The first derivative of y=(sqrt(t))^t is (sqrt(t))^t(ln(sqrt(t))+1/2)