What is the derivative of-3cos(x+xsin(x)) ?

The derivative of-3cos(x+xsin(x)) is 4sin(x)+xcos(x)

What is the first derivative of-3cos(x+xsin(x)) ?

The first derivative of-3cos(x+xsin(x)) is 4sin(x)+xcos(x)

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\frac{d}{d x} (- 3 cos (x) + x sin (x))

4 sin (x) + x cos (x)

Solution steps

\frac{d}{d x} (- 3 cos (x) + x sin (x))

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (3 cos (x)) + \frac{d}{d x} (x sin (x))

\frac{d}{d x} (3 cos (x)) = - 3 sin (x)

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

= - (- 3 sin (x)) + sin (x) + x cos (x)

Simplify

= 4 sin (x) + x cos (x)

y^{^{'}} (y^{3} - x) = y

\int \frac{1}{x + 9} d x

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

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y (0) = 2, y^{^{'}} (0) = - 7

\int_{- 1}^{1} \frac{1}{x ^{\frac{2}{3}}} d x

What is the derivative of-3cos(x+xsin(x)) ?
The derivative of-3cos(x+xsin(x)) is 4sin(x)+xcos(x)
What is the first derivative of-3cos(x+xsin(x)) ?
The first derivative of-3cos(x+xsin(x)) is 4sin(x)+xcos(x)