What is the derivative of x+sin(y) ?

The derivative of x+sin(y) is 1+cos(y)(dy)/(dx)

What is the first derivative of x+sin(y) ?

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

\int \frac{9 x ^{3} - 6 x + 4}{x ^{3} - x ^{2}} d x

\frac{\partial}{\partial t} (e^{- 2 t} cos (2 x))

\int (2 e^{3 x}) d x

\int (4 x^{2} + \frac{1}{( 4 x ) ^{2}}) d x

y^{^{'}} = 9 x 7 y + 8, y (0) = 3

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