What is expand (y^2+5x^3) derivative of+xy ?

The solution to expand (y^2+5x^3) derivative of+xy is y^2 derivative of yx+5x^3 derivative of yx

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expand (y^2+5x^3) derivative of+xy

expand

(y^{2} + 5 x^{3}) \frac{d}{d x} (+ x y)

y^{2} \frac{d}{d x} (y x) + 5 x^{3} \frac{d}{d x} (y x)

Solution steps

(y^{2} + 5 x^{3}) \frac{d}{d x} (x y)

= (y^{2} + 5 x^{3}) \frac{d}{d x} (y x)

Apply the distributive law:

a (b + c) = ab + a c

a = \frac{d}{d x} (x y), b = y^{2}, c = 5 x^{3}

= \frac{d}{d x} (x y) y^{2} + \frac{d}{d x} (x y) 5 x^{3}

= y^{2} \frac{d}{d x} (y x) + 5 x^{3} \frac{d}{d x} (y x)

5 (2 e^{x} + \frac{1}{4} e^{4 x}) + C

(1 + tan (x)) \cdot (1 + co tan (x))

(x - 3) (x + 12 + \frac{29}{x - 3})

\frac{5 ( 2 - x ^{2} ) ^{2}}{2}

What is expand (y^2+5x^3) derivative of+xy ?
The solution to expand (y^2+5x^3) derivative of+xy is y^2 derivative of yx+5x^3 derivative of yx