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Popular >

d/(dt)(A(e^{-t}-e^{-t}t))

Solution

\frac{d}{d t} (A (e^{- t} - e^{- t} t))

Solution

A (e^{- t} t - 2 e^{- t})

Solution steps

\frac{d}{d t} (A (e^{- t} - e^{- t} t))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

= A (- e^{- t} - (- e^{- t} t + e^{- t}))

Simplify

= A (e^{- t} t - 2 e^{- t})

Graph

Popular Examples

derivative of ln(3^{sqrt(2-x^2)})

\frac{d}{d x} (ln (3^{2 - x^{2}}))

integral from-1 to 0 of 1/(sqrt(1+x))

\int_{- 1}^{0} \frac{1}{1 + x} d x

(\partial)/(\partial x)(x^9)

\frac{\partial}{\partial x} (x^{9})

tangent of y=4x^3,(-1,-4)tangent of

y = 4 x^{3}, (- 1, - 4)

limit as x approaches 1/2 of (x+1)/(x+5)

x \to \frac{1}{2} lim (\frac{x + 1}{x + 5})

Frequently Asked Questions (FAQ)

What is the d/(dt)(A(e^{-t}-e^{-t}t)) ?
The d/(dt)(A(e^{-t}-e^{-t}t)) is A(e^{-t}t-2e^{-t})
What is the first d/(dt)(A(e^{-t}-e^{-t}t)) ?
The first d/(dt)(A(e^{-t}-e^{-t}t)) is A(e^{-t}t-2e^{-t})