What is the d/(dy)(e^{3x}(3x^2y+2xy+y^3)) ?

The d/(dy)(e^{3x}(3x^2y+2xy+y^3)) is e^{3x}(3x^2+2x+3y^2)

What is the first d/(dy)(e^{3x}(3x^2y+2xy+y^3)) ?

The first d/(dy)(e^{3x}(3x^2y+2xy+y^3)) is e^{3x}(3x^2+2x+3y^2)

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Popular >

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

e^{3 x} (3 x^{2} + 2 x + 3 y^{2})

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= e^{3 x} (3 x^{2} + 2 x + 3 y^{2})

\int \frac{cos ( 3 t ) + 3}{sin ( 3 t )} d t

\int \frac{2 ln ( x )}{x ^{3}} d x

\int 2 x + 6 d x

\frac{1}{s ^{4} ( s + 3 )}

\frac{\partial}{\partial z} (\frac{z}{x ^{2} + y ^{2} + z ^{2}})

What is the d/(dy)(e^{3x}(3x^2y+2xy+y^3)) ?
The d/(dy)(e^{3x}(3x^2y+2xy+y^3)) is e^{3x}(3x^2+2x+3y^2)
What is the first d/(dy)(e^{3x}(3x^2y+2xy+y^3)) ?
The first d/(dy)(e^{3x}(3x^2y+2xy+y^3)) is e^{3x}(3x^2+2x+3y^2)