What is the derivative of 2(xsin(x)+cos(x)) ?

The derivative of 2(xsin(x)+cos(x)) is 2xcos(x)

What is the first derivative of 2(xsin(x)+cos(x)) ?

The first derivative of 2(xsin(x)+cos(x)) is 2xcos(x)

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derivative of

2 (x sin (x) + cos (x))

2 x cos (x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

= 2 (\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)

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

Simplify

= 2 x cos (x)

\frac{1}{3 x ^{2} + 2}

\frac{( cos ( x ) - cos ^{3} ( x ) )}{x ^{2}}

\frac{6}{2 - 4 x}

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

\frac{50}{( x + 5 )}

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