What is the derivative of (Ax^2+Bx*sin(x)) ?

The derivative of (Ax^2+Bx*sin(x)) is (2Ax+B)sin(x)+cos(x)(Ax^2+Bx)

What is the first derivative of (Ax^2+Bx*sin(x)) ?

The first derivative of (Ax^2+Bx*sin(x)) is (2Ax+B)sin(x)+cos(x)(Ax^2+Bx)

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\frac{d}{d x} ((A x^{2} + B x) \cdot sin (x))

(2 A x + B) sin (x) + cos (x) (A x^{2} + B x)

Solution steps

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

Treat

A, B

as constants

Apply the Product Rule:

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

f = A x^{2} + B x, g = sin (x)

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

\frac{d}{d x} (A x^{2} + B x) = 2 A x + B

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

= (2 A x + B) sin (x) + cos (x) (A x^{2} + B x)

What is the derivative of (Ax^2+Bx*sin(x)) ?
The derivative of (Ax^2+Bx*sin(x)) is (2Ax+B)sin(x)+cos(x)(Ax^2+Bx)
What is the first derivative of (Ax^2+Bx*sin(x)) ?
The first derivative of (Ax^2+Bx*sin(x)) is (2Ax+B)sin(x)+cos(x)(Ax^2+Bx)