What is (\partial)/(\partial x)((2x^2-5x)^3(2x+1)) ?

The answer to (\partial)/(\partial x)((2x^2-5x)^3(2x+1)) is 3(2x^2-5x)^2(4x-5)(2x+1)+2(2x^2-5x)^3

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(\partial)/(\partial x)((2x^2-5x)^3(2x+1))

\frac{\partial}{\partial x} ((2 x^{2} - 5 x)^{3} (2 x + 1))

3 (2 x^{2} - 5 x)^{2} (4 x - 5) (2 x + 1) + 2 (2 x^{2} - 5 x)^{3}

Solution steps

\frac{\partial}{\partial x} ((2 x^{2} - 5 x)^{3} (2 x + 1))

Apply the Product Rule:

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

f = (2 x^{2} - 5 x)^{3}, g = 2 x + 1

= \frac{\partial}{\partial x} ((2 x^{2} - 5 x)^{3}) (2 x + 1) + \frac{\partial}{\partial x} (2 x + 1) (2 x^{2} - 5 x)^{3}

\frac{\partial}{\partial x} ((2 x^{2} - 5 x)^{3}) = 3 (2 x^{2} - 5 x)^{2} (4 x - 5)

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

= 3 (2 x^{2} - 5 x)^{2} (4 x - 5) (2 x + 1) + 2 (2 x^{2} - 5 x)^{3}

s \to \infty lim (c t)

x = y, x = 2, y = 0

\frac{d y}{d x} = \frac{1}{1 - x ^{2}}

What is (\partial)/(\partial x)((2x^2-5x)^3(2x+1)) ?
The answer to (\partial)/(\partial x)((2x^2-5x)^3(2x+1)) is 3(2x^2-5x)^2(4x-5)(2x+1)+2(2x^2-5x)^3