What is the derivative of y(x+1) ?

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

What is the first derivative of y(x+1) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = y, g = x + 1

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

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

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

Simplify

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

\int (2 + x^{2})^{2} d x

\frac{\partial}{\partial x} (sin (x y))

\int_{0}^{4} x e^{- x} d x

y = x^{3}, y = 8, x = - 1

x \to 0 lim (2^{x})

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