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Popular >

derivative of sin(x+3+(-cos(x-1/2)))

Solution

\frac{d}{d x} (sin (x + 3) + (- cos (x - \frac{1}{2})))

Solution

cos (x + 3) + sin (x - \frac{1}{2})

Solution steps

\frac{d}{d x} (sin (x + 3) + (- cos (x - \frac{1}{2})))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin (x + 3)) - \frac{d}{d x} (cos (x - \frac{1}{2}))

\frac{d}{d x} (sin (x + 3)) = cos (x + 3)

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

= cos (x + 3) - (- sin (x - \frac{1}{2}))

Simplify

= cos (x + 3) + sin (x - \frac{1}{2})

Popular Examples

integral from-2 to-1 of 6x^{-3}

\int_{- 2}^{- 1} 6 x^{- 3} d x

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

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

derivative of (x^2+2/(x^4-3x^2+1))

\frac{d}{d x} (\frac{x ^{2} + 2}{x ^{4} - 3 x ^{2} + 1})

y^{''}-4y^'+13y=0,y(0)=1,y^'(0)=4

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = 1, y^{^{'}} (0) = 4

integral of sqrt(x^2+1)x

\int x^{2} + 1 x d x

Frequently Asked Questions (FAQ)

What is the derivative of sin(x+3+(-cos(x-1/2))) ?
The derivative of sin(x+3+(-cos(x-1/2))) is cos(x+3)+sin(x-1/2)
What is the first derivative of sin(x+3+(-cos(x-1/2))) ?
The first derivative of sin(x+3+(-cos(x-1/2))) is cos(x+3)+sin(x-1/2)