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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

Popular Examples

tangent of y=x^4+8x^2-x tangent of

y = x^{4} + 8 x^{2} - x

integral of 4*sin(2x)-3*cos(3x)

\int 4 \cdot sin (2 x) - 3 \cdot cos (3 x) d x

integral of 15x^{17}e^{x^9}

\int 15 x^{17} e^{x^{9}} d x

limit as x approaches 4 of 3(x^2)/2

x \to 4 lim (3 \frac{x ^{2}}{2})

tangent of f(x)= 1/(x^5),(-3,-1/243)tangent of

f (x) = \frac{1}{x ^{5}}, (- 3, - \frac{1}{243})

Frequently Asked Questions (FAQ)

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