What is the derivative of x^2sin(x+2xcos(x)-2sin(x)) ?

The derivative of x^2sin(x+2xcos(x)-2sin(x)) is (2x+cot(x)(x^2-2))/(csc(x))+2(cos(x)-xsin(x))

What is the first derivative of x^2sin(x+2xcos(x)-2sin(x)) ?

The first derivative of x^2sin(x+2xcos(x)-2sin(x)) is (2x+cot(x)(x^2-2))/(csc(x))+2(cos(x)-xsin(x))

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

\frac{2 x + cot ( x ) ( x ^{2} - 2 )}{csc ( x )} + 2 (cos (x) - x sin (x))

Solution steps

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

Simplify

x^{2} sin (x) + 2 x cos (x) - 2 sin (x) : \frac{- 2 + x ^{2}}{csc ( x )} + 2 x cos (x)

= \frac{d}{d x} (\frac{- 2 + x ^{2}}{csc ( x )} + 2 x cos (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{- 2 + x ^{2}}{csc ( x )}) + \frac{d}{d x} (2 x cos (x))

\frac{d}{d x} (\frac{- 2 + x ^{2}}{csc ( x )}) = \frac{2 x + cot ( x ) ( x ^{2} - 2 )}{csc ( x )}

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

= \frac{2 x + cot ( x ) ( x ^{2} - 2 )}{csc ( x )} + 2 (cos (x) - x sin (x))

\int_{9}^{16} \frac{1}{9 - x} d x

\frac{d}{d x} (- \frac{11}{( x - 3 ) ^{2}})

\frac{\partial}{\partial x} (x y e^{- x - y})

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

\frac{d}{d x} ((cot (x) + csc (x))^{- 1})

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