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

The derivative of (3x-2^2(3-x^2)^2) is 54x^5-60x^4-200x^3+216x^2+114x-108

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

The first derivative of (3x-2^2(3-x^2)^2) is 54x^5-60x^4-200x^3+216x^2+114x-108

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

54 x^{5} - 60 x^{4} - 200 x^{3} + 216 x^{2} + 114 x - 108

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

6 (3 x - 2) (3 - x^{2})^{2} + (- 4 x (3 - x^{2})) (3 x - 2)^{2} : 54 x^{5} - 60 x^{4} - 200 x^{3} + 216 x^{2} + 114 x - 108

= 54 x^{5} - 60 x^{4} - 200 x^{3} + 216 x^{2} + 114 x - 108

y = (e^{x} + x)^{5}

f (x) = 2^{4 x} + 4 x^{2}

y^{^{'}} + x y = x y^{3}

\frac{d y}{d x}, 5 x y = 8

x \to 0 lim (\frac{x}{x + 7})

What is the derivative of (3x-2^2(3-x^2)^2) ?
The derivative of (3x-2^2(3-x^2)^2) is 54x^5-60x^4-200x^3+216x^2+114x-108
What is the first derivative of (3x-2^2(3-x^2)^2) ?
The first derivative of (3x-2^2(3-x^2)^2) is 54x^5-60x^4-200x^3+216x^2+114x-108