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

The derivative of dcos(x+x^2sin(x)) is -dsin(x)+2xsin(x)+cos(x)x^2

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

The first derivative of dcos(x+x^2sin(x)) is -dsin(x)+2xsin(x)+cos(x)x^2

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

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

Solution steps

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

Treat

d

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

What is the derivative of dcos(x+x^2sin(x)) ?
The derivative of dcos(x+x^2sin(x)) is -dsin(x)+2xsin(x)+cos(x)x^2
What is the first derivative of dcos(x+x^2sin(x)) ?
The first derivative of dcos(x+x^2sin(x)) is -dsin(x)+2xsin(x)+cos(x)x^2