What is the d/(dt)(t^{sqrt(3t)}) ?

The d/(dt)(t^{sqrt(3t)}) is sqrt(3)t^{sqrt(3)sqrt(t)}((ln(t))/(2sqrt(t))+1/(sqrt(t)))

What is the first d/(dt)(t^{sqrt(3t)}) ?

The first d/(dt)(t^{sqrt(3t)}) is sqrt(3)t^{sqrt(3)sqrt(t)}((ln(t))/(2sqrt(t))+1/(sqrt(t)))

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

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

Solution steps

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

Simplify

t^{3 t} : t^{3 t}

= \frac{d}{d t} (t^{3 t})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

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

\frac{d}{d x} (\frac{6}{x ^{2} + 3})

x \to - 2 lim (x + 4)

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

\frac{d}{d x} (\frac{3}{2 x})

What is the d/(dt)(t^{sqrt(3t)}) ?
The d/(dt)(t^{sqrt(3t)}) is sqrt(3)t^{sqrt(3)sqrt(t)}((ln(t))/(2sqrt(t))+1/(sqrt(t)))
What is the first d/(dt)(t^{sqrt(3t)}) ?
The first d/(dt)(t^{sqrt(3t)}) is sqrt(3)t^{sqrt(3)sqrt(t)}((ln(t))/(2sqrt(t))+1/(sqrt(t)))