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Popular >

derivative of 2x^2-1+ce^{-2x^2}

Solution

\frac{d}{d x} (2 x^{2} - 1 + c e^{- 2 x^{2}})

Solution

4 x - 4 c e^{- 2 x^{2}} x

Solution steps

\frac{d}{d x} (2 x^{2} - 1 + c e^{- 2 x^{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x^{2}) - \frac{d}{d x} (1) + \frac{d}{d x} (c e^{- 2 x^{2}})

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

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

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

= 4 x - 0 - 4 c e^{- 2 x^{2}} x

Simplify

= 4 x - 4 c e^{- 2 x^{2}} x

Graph

Popular Examples

(\partial)/(\partial x)(xyz+x^3+y^4+z^5)

\frac{\partial}{\partial x} (x yz + x^{3} + y^{4} + z^{5})

y^{''}+y=t(1+sin(t))

y^{^{''}} + y = t (1 + sin (t))

derivative of f(x)=sqrt(x^4+x^2+2)derivative of

f (x) = x^{4} + x^{2} + 2

limit as x approaches 4 of (ax^4)/(x-4)

x \to 4 lim (\frac{a x ^{4}}{x - 4})

integral of e^{5x}x

\int e^{5 x} x d x

Frequently Asked Questions (FAQ)

What is the derivative of 2x^2-1+ce^{-2x^2} ?
The derivative of 2x^2-1+ce^{-2x^2} is 4x-4ce^{-2x^2}x
What is the first derivative of 2x^2-1+ce^{-2x^2} ?
The first derivative of 2x^2-1+ce^{-2x^2} is 4x-4ce^{-2x^2}x