What is the derivative of (4x+3)(x^2-1)^2 ?

The derivative of (4x+3)(x^2-1)^2 is 20x^4+12x^3-24x^2-12x+4

What is the first derivative of (4x+3)(x^2-1)^2 ?

The first derivative of (4x+3)(x^2-1)^2 is 20x^4+12x^3-24x^2-12x+4

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derivative of

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

20 x^{4} + 12 x^{3} - 24 x^{2} - 12 x + 4

Solution steps

\frac{d}{d x} ((4 x + 3) (x^{2} - 1)^{2})

Apply the Product Rule:

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

f = 4 x + 3, g = (x^{2} - 1)^{2}

= \frac{d}{d x} (4 x + 3) (x^{2} - 1)^{2} + \frac{d}{d x} ((x^{2} - 1)^{2}) (4 x + 3)

\frac{d}{d x} (4 x + 3) = 4

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

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

Simplify

4 (x^{2} - 1)^{2} + 4 x (x^{2} - 1) (4 x + 3) : 20 x^{4} + 12 x^{3} - 24 x^{2} - 12 x + 4

= 20 x^{4} + 12 x^{3} - 24 x^{2} - 12 x + 4

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

x \to e lim (\frac{1}{2} ln (x))

\frac{d}{d x} (sin ((π x)^{9}))

f (x) = 8 x - 10, (4, 22)

x^{^{''}} + \frac{4}{5} x^{^{'}} + 4 x = 5, x (0) = 0, x^{^{'}} (0) = 0

What is the derivative of (4x+3)(x^2-1)^2 ?
The derivative of (4x+3)(x^2-1)^2 is 20x^4+12x^3-24x^2-12x+4
What is the first derivative of (4x+3)(x^2-1)^2 ?
The first derivative of (4x+3)(x^2-1)^2 is 20x^4+12x^3-24x^2-12x+4