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Popular >

derivative of 7sin(xe^{-x}-1)

Solution

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

Solution

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))

Graph

Popular Examples

(\partial)/(\partial x)(e^{2x}-xcos(xy))

\frac{\partial}{\partial x} (e^{2 x} - x cos (x y))

derivative of 4x^2-2x

\frac{d}{d x} (4 x^{2} - 2 x)

integral of 1/(x^3-x)

\int \frac{1}{x ^{3} - x} d x

2y^{''}+y^'+3y=3cos(3t)+2sin(3t)

2 y^{^{''}} + y^{^{'}} + 3 y = 3 cos (3 t) + 2 sin (3 t)

integral of 3/(1+t^2)

\int \frac{3}{1 + t ^{2}} d t

Frequently Asked Questions (FAQ)

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))