What is the derivative of yx ?

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

What is the first derivative of yx ?

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

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

x \frac{d y}{d x} + y

Solution steps

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

Apply the Product Rule:

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

f = y, g = x

= \frac{d y}{d x} x + \frac{d x}{d x} y

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

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

Simplify

= x \frac{d y}{d x} + y

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = \frac{- 6 x}{x ^{2} + 1}, (1, - 3)

y^{^{'}} = y (1 - 0.001 y)

\int_{0}^{1} π (x^{2})^{2} d x

\frac{d}{d t} (6 t)