What is (\partial)/(\partial x)((3x-1)^2(x^3+1)^2) ?

The answer to (\partial)/(\partial x)((3x-1)^2(x^3+1)^2) is 72x^7-42x^6+6x^5+90x^4-48x^3+6x^2+18x-6

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(\partial)/(\partial x)((3x-1)^2(x^3+1)^2)

\frac{\partial}{\partial x} ((3 x - 1)^{2} (x^{3} + 1)^{2})

72 x^{7} - 42 x^{6} + 6 x^{5} + 90 x^{4} - 48 x^{3} + 6 x^{2} + 18 x - 6

Solution steps

\frac{\partial}{\partial x} ((3 x - 1)^{2} (x^{3} + 1)^{2})

Apply the Product Rule:

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

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

= \frac{\partial}{\partial x} ((3 x - 1)^{2}) (x^{3} + 1)^{2} + \frac{\partial}{\partial x} ((x^{3} + 1)^{2}) (3 x - 1)^{2}

\frac{\partial}{\partial x} ((3 x - 1)^{2}) = 6 (3 x - 1)

\frac{\partial}{\partial x} ((x^{3} + 1)^{2}) = 6 x^{2} (x^{3} + 1)

= 6 (3 x - 1) (x^{3} + 1)^{2} + 6 x^{2} (x^{3} + 1) (3 x - 1)^{2}

Simplify

6 (3 x - 1) (x^{3} + 1)^{2} + 6 x^{2} (x^{3} + 1) (3 x - 1)^{2} : 72 x^{7} - 42 x^{6} + 6 x^{5} + 90 x^{4} - 48 x^{3} + 6 x^{2} + 18 x - 6

= 72 x^{7} - 42 x^{6} + 6 x^{5} + 90 x^{4} - 48 x^{3} + 6 x^{2} + 18 x - 6

y = (x + 3)^{3}

\frac{d y}{d t} = - \frac{y}{t}

\int \frac{6}{x ^{2} - 1} d x

f (x) = 4 x^{2} sin (x) - 7 x

\int_{0}^{5} \frac{1}{3 x + 1} d x

What is (\partial)/(\partial x)((3x-1)^2(x^3+1)^2) ?
The answer to (\partial)/(\partial x)((3x-1)^2(x^3+1)^2) is 72x^7-42x^6+6x^5+90x^4-48x^3+6x^2+18x-6