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Popular >

derivative of 1+2sin((x^2/2))

Solution

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

Solution

2 x cos (\frac{x ^{2}}{2})

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 2 cos (\frac{x ^{2}}{2}) x

Simplify

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

Popular Examples

integral of 4/(x^2+16)

\int \frac{4}{x ^{2} + 16} d x

integral of (2(x+2))/5

\int \frac{2 ( x + 2 )}{5} d x

tangent of f(x)=(x^3+2)/3 ,\at x=-3 tangent of

f (x) = \frac{x ^{3} + 2}{3}, at x = - 3

derivative of x^4+y^4

\frac{d}{d x} (x^{4} + y^{4})

derivative of x/(x^3+1)

\frac{d}{d x} (\frac{x}{x ^{3} + 1})

Frequently Asked Questions (FAQ)

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