What is the derivative of y=(x^2+1)sin(x) ?

The derivative of y=(x^2+1)sin(x) is 2xsin(x)+cos(x)(x^2+1)

What is the first derivative of y=(x^2+1)sin(x) ?

The first derivative of y=(x^2+1)sin(x) is 2xsin(x)+cos(x)(x^2+1)

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derivative of

y = (x^{2} + 1) sin (x)

2 x sin (x) + cos (x) (x^{2} + 1)

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + 1, g = sin (x)

= \frac{d}{d x} (x^{2} + 1) sin (x) + \frac{d}{d x} (sin (x)) (x^{2} + 1)

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

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

= 2 x sin (x) + cos (x) (x^{2} + 1)

2 cos^{2} (x) - 1

\frac{1}{2 ^{x}}

(1 + 2 x)^{x}

\frac{( x ^{2} - x + 1 )}{( a ^{3} - 3 )}

\frac{d}{d t} (a^{2} t)

What is the derivative of y=(x^2+1)sin(x) ?
The derivative of y=(x^2+1)sin(x) is 2xsin(x)+cos(x)(x^2+1)
What is the first derivative of y=(x^2+1)sin(x) ?
The first derivative of y=(x^2+1)sin(x) is 2xsin(x)+cos(x)(x^2+1)