What is expand (e^{4x})(x^2(dy)/(dx)+2xy) ?

The solution to expand (e^{4x})(x^2(dy)/(dx)+2xy) is e^{4x}x^2(dy)/(dx)+2e^{4x}xy

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expand (e^{4x})(x^2(dy)/(dx)+2xy)

expand

(e^{4 x}) (x^{2} \frac{d y}{d x} + 2 x y)

e^{4 x} x^{2} \frac{d y}{d x} + 2 e^{4 x} x y

Solution steps

(e^{4 x}) (x^{2} \frac{d y}{d x} + 2 x y)

Apply the distributive law:

a (b + c) = ab + a c

a = (e^{4 x}), b = x^{2} \frac{d y}{d x}, c = 2 x y

= (e^{4 x}) x^{2} \frac{d y}{d x} + (e^{4 x}) \cdot 2 x y

= x^{2} (e^{4 x}) \frac{d y}{d x} + 2 x y (e^{4 x})

Remove parentheses:

(a) = a

= e^{4 x} x^{2} \frac{d y}{d x} + 2 e^{4 x} x y

\frac{1}{( A \cdot x ^{2} + 1 ) \cdot x ^{2}}

\frac{d}{d t} ((a (t)) (a (t)^{4} + t^{4} - 6 a (t)^{2} t))

\frac{j + 2}{( - 2 + j ) ( j - 1 ) ( j ^{2} + 2 j + 5 )}

s q r 1 + \frac{1}{( 9 x ^{\frac{4}{3}} )}

(3^{^{'}} x^{2^{^{'}}} - 6 x + 4) (- 2 x^{2} + 7 x + 5)^{^{'}}

What is expand (e^{4x})(x^2(dy)/(dx)+2xy) ?
The solution to expand (e^{4x})(x^2(dy)/(dx)+2xy) is e^{4x}x^2(dy)/(dx)+2e^{4x}xy