What is the derivative of x^2(1+y^3) ?

The derivative of x^2(1+y^3) is 2x(1+y)^3+3(1+y)^2(dy)/(dx)x^2

What is the first derivative of x^2(1+y^3) ?

The first derivative of x^2(1+y^3) is 2x(1+y)^3+3(1+y)^2(dy)/(dx)x^2

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = (1 + y)^{3}

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

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

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

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

\frac{d}{d x} (cos^{l n (7 x)} (x))

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

\int (x)^{2} d x

y = 4 - e^{x}

\int \frac{1}{x} (x + 1)^{2} d x

What is the derivative of x^2(1+y^3) ?
The derivative of x^2(1+y^3) is 2x(1+y)^3+3(1+y)^2(dy)/(dx)x^2
What is the first derivative of x^2(1+y^3) ?
The first derivative of x^2(1+y^3) is 2x(1+y)^3+3(1+y)^2(dy)/(dx)x^2