What is the derivative of 7sin(xe^{-x}-1) ?

The derivative of 7sin(xe^{-x}-1) is 7(e^{-x}cos(x)-e^{-x}sin(x))

What is the first derivative of 7sin(xe^{-x}-1) ?

The first derivative of 7sin(xe^{-x}-1) is 7(e^{-x}cos(x)-e^{-x}sin(x))

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\frac{d}{d x} (7 sin (x) e^{- x} - 1)

7 (e^{- x} cos (x) - e^{- x} sin (x))

Solution steps

\frac{d}{d x} (7 sin (x) e^{- x} - 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (7 sin (x) e^{- x}) - \frac{d}{d x} (1)

\frac{d}{d x} (7 sin (x) e^{- x}) = 7 (e^{- x} cos (x) - e^{- x} sin (x))

\frac{d}{d x} (1) = 0

= 7 (e^{- x} cos (x) - e^{- x} sin (x)) - 0

Simplify

= 7 (e^{- x} cos (x) - e^{- x} sin (x))

What is the derivative of 7sin(xe^{-x}-1) ?
The derivative of 7sin(xe^{-x}-1) is 7(e^{-x}cos(x)-e^{-x}sin(x))
What is the first derivative of 7sin(xe^{-x}-1) ?
The first derivative of 7sin(xe^{-x}-1) is 7(e^{-x}cos(x)-e^{-x}sin(x))