What is the d/(du)(x^2+x{y}(x,u)(x,u)^3) ?

The d/(du)(x^2+x{y}(x,u)(x,u)^3) is 0+x(d/(du)({y}(x,u))(x,u)^3+3(x,u)^2(x,1){y}(x,u))

What is the first d/(du)(x^2+x{y}(x,u)(x,u)^3) ?

The first d/(du)(x^2+x{y}(x,u)(x,u)^3) is 0+x(d/(du)({y}(x,u))(x,u)^3+3(x,u)^2(x,1){y}(x,u))

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\frac{d}{d u} (x^{2} + x y (x, u) (x, u)^{3})

0 + x (\frac{d}{d u} (y (x, u)) (x, u)^{3} + 3 (x, u)^{2} (x, 1) y (x, u))

Solution steps

\frac{d}{d u} (x^{2} + x y (x, u) (x, u)^{3})

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d u} (x^{2}) + \frac{d}{d u} (x y (x, u) (x, u)^{3})

\frac{d}{d u} (x^{2}) = 0

\frac{d}{d u} (x y (x, u) (x, u)^{3}) = x (\frac{d}{d u} (y (x, u)) (x, u)^{3} + 3 (x, u)^{2} (x, 1) y (x, u))

= 0 + x (\frac{d}{d u} (y (x, u)) (x, u)^{3} + 3 (x, u)^{2} (x, 1) y (x, u))

\int t ln (t) d t

\int x^{\frac{5}{4}} d x

t^{2} \frac{d ^{2} y}{d t ^{2}} + 2 t \frac{d y}{d t} - 6 y = 0

t an g e n t (x + 2)^{2} + (y - 3)^{2} = 37, (- 8, 4)

\int cos^{2} (u) sin^{2} (u) d u

What is the d/(du)(x^2+x{y}(x,u)(x,u)^3) ?
The d/(du)(x^2+x{y}(x,u)(x,u)^3) is 0+x(d/(du)({y}(x,u))(x,u)^3+3(x,u)^2(x,1){y}(x,u))
What is the first d/(du)(x^2+x{y}(x,u)(x,u)^3) ?
The first d/(du)(x^2+x{y}(x,u)(x,u)^3) is 0+x(d/(du)({y}(x,u))(x,u)^3+3(x,u)^2(x,1){y}(x,u))