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derivative of e^{-x^2}-sin(xcos(x))

Solution

\frac{d}{d x} (e^{- x^{2}} - sin (x) cos (x))

Solution

- 2 e^{- x^{2}} x - cos (2 x)

Solution steps

\frac{d}{d x} (e^{- x^{2}} - sin (x) cos (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{- x^{2}}) - \frac{d}{d x} (sin (x) cos (x))

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

\frac{d}{d x} (sin (x) cos (x)) = cos (2 x)

= - 2 e^{- x^{2}} x - cos (2 x)

Popular Examples

(\partial)/(\partial x)(ln(2x^3+y))

\frac{\partial}{\partial x} (ln (2 x^{3} + y))

derivative of f(x)=(-25x^2+9)^2 derivative of

f (x) = (- 25 x^{2} + 9)^{2}

(\partial)/(\partial x)(1-x-y)

\frac{\partial}{\partial x} (1 - x - y)

inverse oflaplace 4/(s+2)inverse laplace

\frac{4}{s + 2}

integral of (2000)/(1+0.3e^{-0.276t)}

\int \frac{2000}{1 + 0.3 e ^{- 0.276 t}} d t

Frequently Asked Questions (FAQ)

What is the derivative of e^{-x^2}-sin(xcos(x)) ?
The derivative of e^{-x^2}-sin(xcos(x)) is -2e^{-x^2}x-cos(2x)
What is the first derivative of e^{-x^2}-sin(xcos(x)) ?
The first derivative of e^{-x^2}-sin(xcos(x)) is -2e^{-x^2}x-cos(2x)