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Popular >

derivative of (x+ysin(y))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x + y, g = sin (y)

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

\frac{d}{d x} (x + y) = 1 + \frac{d y}{d x}

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

= (1 + \frac{d y}{d x}) sin (y) + cos (y) \frac{d y}{d x} (x + y)

Popular Examples

integral of ln(e^{-x^2})

\int ln (e^{- x^{2}}) d x

area 5x^4-5x^2,9x^2 area

5 x^{4} - 5 x^{2}, 9 x^{2}

integral of (x^2)/(9e^{3x)}

\int \frac{x ^{2}}{9 e ^{3 x}} d x

derivative of y=(8x)/(5-tan(x))derivative of

y = \frac{8 x}{5 - tan ( x )}

integral of sin^3(2x)cos^5(2x)

\int sin^{3} (2 x) cos^{5} (2 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (x+ysin(y)) ?
The derivative of (x+ysin(y)) is (1+(dy)/(dx))sin(y)+cos(y)(dy)/(dx)(x+y)
What is the first derivative of (x+ysin(y)) ?
The first derivative of (x+ysin(y)) is (1+(dy)/(dx))sin(y)+cos(y)(dy)/(dx)(x+y)