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Popular >

derivative of (y(sin(x)+x^2))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of (y(sin(x)+x^2)) ?
The derivative of (y(sin(x)+x^2)) is (dy)/(dx)(sin(x)+x^2)+(cos(x)+2x)y
What is the first derivative of (y(sin(x)+x^2)) ?
The first derivative of (y(sin(x)+x^2)) is (dy)/(dx)(sin(x)+x^2)+(cos(x)+2x)y