What is the derivative of (2ya-xy^2) ?

The derivative of (2ya-xy^2) is -2xy(dy)/(dx)+6ay(x)^2(dy)/(dx)-y^2

What is the first derivative of (2ya-xy^2) ?

The first derivative of (2ya-xy^2) is -2xy(dy)/(dx)+6ay(x)^2(dy)/(dx)-y^2

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

- 2 x y \frac{d y}{d x} + 6 a y (x)^{2} \frac{d y}{d x} - y^{2}

Solution steps

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

Apply the Product Rule:

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

f = 2 y a - x, g = y^{2}

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

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

\frac{d}{d x} (y^{2}) = 2 y \frac{d y}{d x}

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

Simplify

(2 a \frac{d y}{d x} - 1) y^{2} + 2 y \frac{d y}{d x} (2 y a - x) : - 2 x y \frac{d y}{d x} + 6 a y (x)^{2} \frac{d y}{d x} - y^{2}

= - 2 x y \frac{d y}{d x} + 6 a y (x)^{2} \frac{d y}{d x} - y^{2}

x^{3} - 7 x^{2} + 15 x + 3

x \to \infty lim (87)

\frac{8}{s ^{2} ( s - 2 ) ^{3}}

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

\int 2 x^{5} - 7 x^{3} + 6 d x

What is the derivative of (2ya-xy^2) ?
The derivative of (2ya-xy^2) is -2xy(dy)/(dx)+6ay(x)^2(dy)/(dx)-y^2
What is the first derivative of (2ya-xy^2) ?
The first derivative of (2ya-xy^2) is -2xy(dy)/(dx)+6ay(x)^2(dy)/(dx)-y^2