What is the derivative of ({Q}(x,y)(x^2+y(x,d)^2)dy(x,d)) ?

The derivative of ({Q}(x,y)(x^2+y(x,d)^2)dy(x,d)) is

What is the first derivative of ({Q}(x,y)(x^2+y(x,d)^2)dy(x,d)) ?

The first derivative of ({Q}(x,y)(x^2+y(x,d)^2)dy(x,d)) is

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\frac{d}{d x} ((Q (x, y)) (x^{2} + y (x, d) (x, d)^{2}) d y (x, d))

d (\frac{d}{d x} (Q (x, y)) (x^{2} + y (x, d) (x, d)^{2}) y (x, d) + ((2 x + (\frac{d}{d x} (y (x, d)) (x, d)^{2} + 2 (x, d) (, d \cdot 1) y (x, d))) y (x, d) + \frac{d}{d x} (y (x, d)) (x^{2} + y (x, d) (x, d)^{2})) Q (x, y))

Solution steps

\frac{d}{d x} ((Q (x, y)) (x^{2} + y (x, d) (x, d)^{2}) d y (x, d))

Treat

d

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = Q (x, y), g = (x^{2} + y (x, d) (x, d)^{2}) y (x, d)

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

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

= d (\frac{d}{d x} (Q (x, y)) (x^{2} + y (x, d) (x, d)^{2}) y (x, d) + ((2 x + (\frac{d}{d x} (y (x, d)) (x, d)^{2} + 2 (x, d) (, d \cdot 1) y (x, d))) y (x, d) + \frac{d}{d x} (y (x, d)) (x^{2} + y (x, d) (x, d)^{2})) Q (x, y))

(e^{\frac{jπ}{2}} - e^{- \frac{jπ}{2}})^{3}

\frac{( 2 x - 1 ) ( 3 - x )}{( x - 1 ) ( x + 3 )}

(0.2 s + 10) \frac{d}{d s} (0.2 s + 10)

I n (\frac{2 x ^{2} y}{z ^{4}})

A (3, - 1, - 2) e B (1, 2, 4)

What is the derivative of ({Q}(x,y)(x^2+y(x,d)^2)dy(x,d)) ?
The derivative of ({Q}(x,y)(x^2+y(x,d)^2)dy(x,d)) is
What is the first derivative of ({Q}(x,y)(x^2+y(x,d)^2)dy(x,d)) ?
The first derivative of ({Q}(x,y)(x^2+y(x,d)^2)dy(x,d)) is