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Popular >

derivative of t^2e^{-t}+(ln(t))^2

Solution

derivative of

t^{2} e^{- t} + (ln (t))^{2}

Solution

2 e^{- t} t - e^{- t} t^{2} + \frac{2 ln ( t )}{t}

Solution steps

\frac{d}{d t} (t^{2} e^{- t} + (ln (t))^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (t^{2} e^{- t}) + \frac{d}{d t} ((ln (t))^{2})

\frac{d}{d t} (t^{2} e^{- t}) = 2 e^{- t} t - e^{- t} t^{2}

\frac{d}{d t} ((ln (t))^{2}) = \frac{2 ln ( t )}{t}

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

Popular Examples

area y=x^2,y= 2/(x^2+1)area

y = x^{2}, y = \frac{2}{x ^{2} + 1}

limit as x approaches 1-of x^3-7+m

x \to 1 - lim (x^{3} - 7 + m)

derivative of f(x)= 3/(2x+5)derivative of

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

y^{^{'}} = 2 y + sin (2 t)

(\partial)/(\partial x)(e^{-(x^3+y^3)})

\frac{\partial}{\partial x} (e^{- (x^{3} + y^{3})})

Frequently Asked Questions (FAQ)

What is the derivative of t^2e^{-t}+(ln(t))^2 ?
The derivative of t^2e^{-t}+(ln(t))^2 is 2e^{-t}t-e^{-t}t^2+(2ln(t))/t
What is the first derivative of t^2e^{-t}+(ln(t))^2 ?
The first derivative of t^2e^{-t}+(ln(t))^2 is 2e^{-t}t-e^{-t}t^2+(2ln(t))/t