What is the derivative of (2x^3-4x^2*(3x^5+x^2)) ?

The derivative of (2x^3-4x^2*(3x^5+x^2)) is 48x^7-84x^6+10x^4-16x^3

What is the first derivative of (2x^3-4x^2*(3x^5+x^2)) ?

The first derivative of (2x^3-4x^2*(3x^5+x^2)) is 48x^7-84x^6+10x^4-16x^3

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\frac{d}{d x} ((2 x^{3} - 4 x^{2}) \cdot (3 x^{5} + x^{2}))

48 x^{7} - 84 x^{6} + 10 x^{4} - 16 x^{3}

Solution steps

\frac{d}{d x} ((2 x^{3} - 4 x^{2}) (3 x^{5} + x^{2}))

Apply the Product Rule:

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

f = 2 x^{3} - 4 x^{2}, g = 3 x^{5} + x^{2}

= \frac{d}{d x} (2 x^{3} - 4 x^{2}) (3 x^{5} + x^{2}) + \frac{d}{d x} (3 x^{5} + x^{2}) (2 x^{3} - 4 x^{2})

\frac{d}{d x} (2 x^{3} - 4 x^{2}) = 6 x^{2} - 8 x

\frac{d}{d x} (3 x^{5} + x^{2}) = 15 x^{4} + 2 x

= (6 x^{2} - 8 x) (3 x^{5} + x^{2}) + (15 x^{4} + 2 x) (2 x^{3} - 4 x^{2})

Simplify

(6 x^{2} - 8 x) (3 x^{5} + x^{2}) + (15 x^{4} + 2 x) (2 x^{3} - 4 x^{2}) : 48 x^{7} - 84 x^{6} + 10 x^{4} - 16 x^{3}

= 48 x^{7} - 84 x^{6} + 10 x^{4} - 16 x^{3}

x \to i lim (\frac{z + i}{z - i})

f (x) = - 2 x^{2} + 8

\int (ln (x) + 4 x) d x

\int (x + 3) 8 - x d x

2 x + \frac{5}{x}

What is the derivative of (2x^3-4x^2*(3x^5+x^2)) ?
The derivative of (2x^3-4x^2*(3x^5+x^2)) is 48x^7-84x^6+10x^4-16x^3
What is the first derivative of (2x^3-4x^2*(3x^5+x^2)) ?
The first derivative of (2x^3-4x^2*(3x^5+x^2)) is 48x^7-84x^6+10x^4-16x^3