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

The derivative of (3x-1)^2(x^2+1)^2 is 54x^5-30x^4+76x^3-36x^2+22x-6

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

The first derivative of (3x-1)^2(x^2+1)^2 is 54x^5-30x^4+76x^3-36x^2+22x-6

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derivative of

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

54 x^{5} - 30 x^{4} + 76 x^{3} - 36 x^{2} + 22 x - 6

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

= 6 (3 x - 1) (x^{2} + 1)^{2} + 4 x (x^{2} + 1) (3 x - 1)^{2}

Simplify

6 (3 x - 1) (x^{2} + 1)^{2} + 4 x (x^{2} + 1) (3 x - 1)^{2} : 54 x^{5} - 30 x^{4} + 76 x^{3} - 36 x^{2} + 22 x - 6

= 54 x^{5} - 30 x^{4} + 76 x^{3} - 36 x^{2} + 22 x - 6

y^{^{'}} - y = 9 t

\int sec^{6} (3 y) tan^{2} (3 y) d y

\frac{\partial}{\partial x} ((2 x) (3 z))

\frac{d y}{d x} = 6 y

\int (cos (x))^{2} - (sin (x))^{2} d x

What is the derivative of (3x-1)^2(x^2+1)^2 ?
The derivative of (3x-1)^2(x^2+1)^2 is 54x^5-30x^4+76x^3-36x^2+22x-6
What is the first derivative of (3x-1)^2(x^2+1)^2 ?
The first derivative of (3x-1)^2(x^2+1)^2 is 54x^5-30x^4+76x^3-36x^2+22x-6