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Popular >

derivative of xsin(x+y)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

Popular Examples

integral of x/(sqrt(x^2+2x+25))

\int \frac{x}{x ^{2} + 2 x + 25} d x

integral of (5x+7)/(4x^2+12x+10)

\int \frac{5 x + 7}{4 x ^{2} + 12 x + 10} d x

derivative of f(t)=((e^x+5x))/(5x)derivative of

f (t) = \frac{( e ^{x} + 5 x )}{5 x}

area x^2+2,2x+6 area

x^{2} + 2, 2 x + 6

integral of 10tan^2(x)

\int 10 tan^{2} (x) d x

Frequently Asked Questions (FAQ)

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