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Popular >

derivative of-xsin(x+cos(x))

Solution

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

Solution

- x cos (x) - 2 sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= - (sin (x) + x cos (x)) - sin (x)

Simplify

= - x cos (x) - 2 sin (x)

Popular Examples

integral of 1/(3+cos(x))

\int \frac{1}{3 + cos ( x )} d x

integral from-pi to pi of |sin(x)|

\int_{- π}^{π} ∣ sin (x) ∣ d x

y^'=(3x-2)(30x+19)

y^{^{'}} = (3 x - 2) (30 x + 19)

(\partial)/(\partial x)(400*sin(x)*cos(x))

\frac{\partial}{\partial x} (400 \cdot sin (x) \cdot cos (x))

(\partial)/(\partial x)(y^2e^{xy^2+z^2})

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

Frequently Asked Questions (FAQ)

What is the derivative of-xsin(x+cos(x)) ?
The derivative of-xsin(x+cos(x)) is -xcos(x)-2sin(x)
What is the first derivative of-xsin(x+cos(x)) ?
The first derivative of-xsin(x+cos(x)) is -xcos(x)-2sin(x)