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

The derivative of (3x^3-2x^2(3x^4+x^2)) is 63x^6-36x^5+15x^4-8x^3

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

The first derivative of (3x^3-2x^2(3x^4+x^2)) is 63x^6-36x^5+15x^4-8x^3

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

63 x^{6} - 36 x^{5} + 15 x^{4} - 8 x^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (3 x^{3} - 2 x^{2}) = 9 x^{2} - 4 x

\frac{d}{d x} (3 x^{4} + x^{2}) = 12 x^{3} + 2 x

= (9 x^{2} - 4 x) (3 x^{4} + x^{2}) + (12 x^{3} + 2 x) (3 x^{3} - 2 x^{2})

Simplify

(9 x^{2} - 4 x) (3 x^{4} + x^{2}) + (12 x^{3} + 2 x) (3 x^{3} - 2 x^{2}) : 63 x^{6} - 36 x^{5} + 15 x^{4} - 8 x^{3}

= 63 x^{6} - 36 x^{5} + 15 x^{4} - 8 x^{3}

\int_{- a}^{a} a^{2} - x^{2} d x

x \to 1 lim (\frac{x ^{2} - 5}{x})

\int y (e^{y}) d y

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

What is the derivative of (3x^3-2x^2(3x^4+x^2)) ?
The derivative of (3x^3-2x^2(3x^4+x^2)) is 63x^6-36x^5+15x^4-8x^3
What is the first derivative of (3x^3-2x^2(3x^4+x^2)) ?
The first derivative of (3x^3-2x^2(3x^4+x^2)) is 63x^6-36x^5+15x^4-8x^3