What is the derivative of t^{sqrt(13t)} ?

The derivative of t^{sqrt(13t)} is sqrt(13)t^{sqrt(13)sqrt(t)}((ln(t))/(2sqrt(t))+1/(sqrt(t)))

What is the first derivative of t^{sqrt(13t)} ?

The first derivative of t^{sqrt(13t)} is sqrt(13)t^{sqrt(13)sqrt(t)}((ln(t))/(2sqrt(t))+1/(sqrt(t)))

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derivative of

t^{13 t}

13 t^{13 t} (\frac{ln ( t )}{2 t} + \frac{1}{t})

Solution steps

\frac{d}{d t} (t^{13 t})

Simplify

t^{13 t} : t^{13 t}

= \frac{d}{d t} (t^{13 t})

Apply exponent rule:

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

t^{13 t} = e^{13 t l n (t)}

= \frac{d}{d t} (e^{13 t l n (t)})

Apply the chain rule:

e^{13 t l n (t)} \frac{d}{d t} (13 t ln (t))

= e^{13 t l n (t)} \frac{d}{d t} (13 t ln (t))

\frac{d}{d t} (13 t ln (t)) = 13 (\frac{ln ( t )}{2 t} + \frac{1}{t})

= e^{13 t l n (t)} 13 (\frac{ln ( t )}{2 t} + \frac{1}{t})

e^{13 t l n (t)} = t^{13 t}

= 13 t^{13 t} (\frac{ln ( t )}{2 t} + \frac{1}{t})

\frac{d}{d x} (sec (5 x) + 1)

f (x) = 4 x^{\frac{5}{4}} + 4 x^{\frac{3}{2}} + 8 x

(x - 1)^{3} \frac{d y}{d x} + 4 (x - 1)^{2} y = x + 1

y^{^{'}} = - \frac{1 + x + y}{1 + x}

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

What is the derivative of t^{sqrt(13t)} ?
The derivative of t^{sqrt(13t)} is sqrt(13)t^{sqrt(13)sqrt(t)}((ln(t))/(2sqrt(t))+1/(sqrt(t)))
What is the first derivative of t^{sqrt(13t)} ?
The first derivative of t^{sqrt(13t)} is sqrt(13)t^{sqrt(13)sqrt(t)}((ln(t))/(2sqrt(t))+1/(sqrt(t)))