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Popular Calculus >

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})

Graph

Popular Examples

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^'=y*tan(x)+sin(x)

y^{^{'}} = y \cdot tan (x) + sin (x)

(\partial)/(\partial x)(xln(x^2y+y^2))

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

integral of (x^8+sec^2(x))

\int (x^{8} + sec^{2} (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)