What is the derivative of (x^3-2x^2+3(7x^2-4x)) ?

The derivative of (x^3-2x^2+3(7x^2-4x)) is 35x^4-72x^3+24x^2+42x-12

What is the first derivative of (x^3-2x^2+3(7x^2-4x)) ?

The first derivative of (x^3-2x^2+3(7x^2-4x)) is 35x^4-72x^3+24x^2+42x-12

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\frac{d}{d x} ((x^{3} - 2 x^{2} + 3) (7 x^{2} - 4 x))

35 x^{4} - 72 x^{3} + 24 x^{2} + 42 x - 12

Solution steps

\frac{d}{d x} ((x^{3} - 2 x^{2} + 3) (7 x^{2} - 4 x))

Apply the Product Rule:

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

f = x^{3} - 2 x^{2} + 3, g = 7 x^{2} - 4 x

= \frac{d}{d x} (x^{3} - 2 x^{2} + 3) (7 x^{2} - 4 x) + \frac{d}{d x} (7 x^{2} - 4 x) (x^{3} - 2 x^{2} + 3)

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

\frac{d}{d x} (7 x^{2} - 4 x) = 14 x - 4

= (3 x^{2} - 4 x) (7 x^{2} - 4 x) + (14 x - 4) (x^{3} - 2 x^{2} + 3)

Simplify

(3 x^{2} - 4 x) (7 x^{2} - 4 x) + (14 x - 4) (x^{3} - 2 x^{2} + 3) : 35 x^{4} - 72 x^{3} + 24 x^{2} + 42 x - 12

= 35 x^{4} - 72 x^{3} + 24 x^{2} + 42 x - 12

\frac{d}{d y} (k y (1 - \frac{y}{N}) (\frac{y}{M} - 1))

\frac{d P}{d t} + P = 10, P (0) = 4

\frac{d y}{d x} = (- \frac{x}{y})

\frac{1}{x ^{\frac{1}{2}}}

\int \frac{x ^{2}}{36 + x ^{2}} d x

What is the derivative of (x^3-2x^2+3(7x^2-4x)) ?
The derivative of (x^3-2x^2+3(7x^2-4x)) is 35x^4-72x^3+24x^2+42x-12
What is the first derivative of (x^3-2x^2+3(7x^2-4x)) ?
The first derivative of (x^3-2x^2+3(7x^2-4x)) is 35x^4-72x^3+24x^2+42x-12