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Popular >

derivative of cos(x-1+1/2 x^2)

Solution

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

Solution

x - sin (x)

Solution steps

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

Simplify

cos (x) - 1 + \frac{1}{2} x^{2} : cos (x) - 1 + \frac{x ^{2}}{2}

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= - sin (x) - 0 + x

Simplify

= x - sin (x)

Popular Examples

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f (x) = \frac{1}{4 x ^{2} + 2 x}

derivative of (x^2+2)(x-5)derivative of

(x^{2} + 2) (x - 5)

(\partial)/(\partial x)((x+1)^2+y^2-1)

\frac{\partial}{\partial x} ((x + 1)^{2} + y^{2} - 1)

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x \to 2 lim (\frac{x ^{2} + 2 x - 8}{3 x - 6})

derivative of \sqrt[3]{sin(x})

Frequently Asked Questions (FAQ)

What is the derivative of cos(x-1+1/2 x^2) ?
The derivative of cos(x-1+1/2 x^2) is x-sin(x)
What is the first derivative of cos(x-1+1/2 x^2) ?
The first derivative of cos(x-1+1/2 x^2) is x-sin(x)