What is the derivative of sin(x-x*cos(x)) ?

The derivative of sin(x-x*cos(x)) is xsin(x)

What is the first derivative of sin(x-x*cos(x)) ?

The first derivative of sin(x-x*cos(x)) is xsin(x)

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

x sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= x sin (x)

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

- csc (x) - sin (x)

- 6 t^{3}

f (x) = x^{3} + 6 x^{2} + x

y^{^{''}} + 2 y^{^{'}} + 10 y = 3 e^{t} + 1

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