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

The derivative of f(x)=(x^2+1)^3-(x^3+1)^2 is 12x^3-6x^2+6x

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

The first derivative of f(x)=(x^2+1)^3-(x^3+1)^2 is 12x^3-6x^2+6x

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derivative of

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

12 x^{3} - 6 x^{2} + 6 x

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

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

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

= 12 x^{3} - 6 x^{2} + 6 x

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

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

\frac{d}{d x} (- 32 cos (2 x))

\frac{x - 3 x x}{x}

\int (2 x y - 9 x^{2}) d x

What is the derivative of f(x)=(x^2+1)^3-(x^3+1)^2 ?
The derivative of f(x)=(x^2+1)^3-(x^3+1)^2 is 12x^3-6x^2+6x
What is the first derivative of f(x)=(x^2+1)^3-(x^3+1)^2 ?
The first derivative of f(x)=(x^2+1)^3-(x^3+1)^2 is 12x^3-6x^2+6x