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

The derivative of sin(x^2cos(pix+2)) is 2xcos(x^2)cos(pix+2)-pisin(pix+2)sin(x^2)

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

The first derivative of sin(x^2cos(pix+2)) is 2xcos(x^2)cos(pix+2)-pisin(pix+2)sin(x^2)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x^{2}), g = cos (π x + 2)

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

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

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

= cos (x^{2}) \cdot 2 x cos (π x + 2) + (- sin (π x + 2) π) sin (x^{2})

Simplify

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

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