What is the derivative of y(x-2) ?

The derivative of y(x-2) is (dy)/(dx)(x-2)+y

What is the first derivative of y(x-2) ?

The first derivative of y(x-2) is (dy)/(dx)(x-2)+y

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\frac{d}{d x} (y (x - 2))

\frac{d y}{d x} (x - 2) + y

Solution steps

\frac{d}{d x} (y (x - 2))

Apply the Product Rule:

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

f = y, g = x - 2

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

\frac{d}{d x} (x - 2) = 1

= \frac{d y}{d x} (x - 2) + 1 \cdot y

Simplify

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

(x^{2} + y^{2}) e^{- (x^{2} + y^{2})}

e^{- 3.66}

e^{2 x} \cdot e^{- 2 x}

(5 m^{6} n^{3}) (6 m^{4} p^{4}) (\frac{1}{3} m p^{5})

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