What is the derivative of (5x-2)^2(4-x^3)^2 ?

The derivative of (5x-2)^2(4-x^3)^2 is 200x^7-140x^6+24x^5-1000x^4+640x^3-96x^2+800x-320

What is the first derivative of (5x-2)^2(4-x^3)^2 ?

The first derivative of (5x-2)^2(4-x^3)^2 is 200x^7-140x^6+24x^5-1000x^4+640x^3-96x^2+800x-320

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derivative of

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

200 x^{7} - 140 x^{6} + 24 x^{5} - 1000 x^{4} + 640 x^{3} - 96 x^{2} + 800 x - 320

Solution steps

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

Apply the Product Rule:

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

f = (5 x - 2)^{2}, g = (4 - x^{3})^{2}

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

\frac{d}{d x} ((5 x - 2)^{2}) = 10 (5 x - 2)

\frac{d}{d x} ((4 - x^{3})^{2}) = - 6 x^{2} (4 - x^{3})

= 10 (5 x - 2) (4 - x^{3})^{2} + (- 6 x^{2} (4 - x^{3})) (5 x - 2)^{2}

Simplify

10 (5 x - 2) (4 - x^{3})^{2} + (- 6 x^{2} (4 - x^{3})) (5 x - 2)^{2} : 200 x^{7} - 140 x^{6} + 24 x^{5} - 1000 x^{4} + 640 x^{3} - 96 x^{2} + 800 x - 320

= 200 x^{7} - 140 x^{6} + 24 x^{5} - 1000 x^{4} + 640 x^{3} - 96 x^{2} + 800 x - 320

f (x) = arctan (x)

\frac{\partial}{\partial x} ((x y)^{x y})

\int 3 - tan (\frac{x}{6}) d x

\frac{\partial}{\partial y} (x y e^{y})

\int \frac{8 x ^{2} + x + 8}{( x ^{2} + 1 ) ^{2}} d x

What is the derivative of (5x-2)^2(4-x^3)^2 ?
The derivative of (5x-2)^2(4-x^3)^2 is 200x^7-140x^6+24x^5-1000x^4+640x^3-96x^2+800x-320
What is the first derivative of (5x-2)^2(4-x^3)^2 ?
The first derivative of (5x-2)^2(4-x^3)^2 is 200x^7-140x^6+24x^5-1000x^4+640x^3-96x^2+800x-320