What is the derivative of (3x^2+19x-7(14x^3+12x)) ?

The derivative of (3x^2+19x-7(14x^3+12x)) is 210x^4+1064x^3-186x^2+456x-84

What is the first derivative of (3x^2+19x-7(14x^3+12x)) ?

The first derivative of (3x^2+19x-7(14x^3+12x)) is 210x^4+1064x^3-186x^2+456x-84

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\frac{d}{d x} ((3 x^{2} + 19 x - 7) (14 x^{3} + 12 x))

210 x^{4} + 1064 x^{3} - 186 x^{2} + 456 x - 84

Solution steps

\frac{d}{d x} ((3 x^{2} + 19 x - 7) (14 x^{3} + 12 x))

Apply the Product Rule:

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

f = 3 x^{2} + 19 x - 7, g = 14 x^{3} + 12 x

= \frac{d}{d x} (3 x^{2} + 19 x - 7) (14 x^{3} + 12 x) + \frac{d}{d x} (14 x^{3} + 12 x) (3 x^{2} + 19 x - 7)

\frac{d}{d x} (3 x^{2} + 19 x - 7) = 6 x + 19

\frac{d}{d x} (14 x^{3} + 12 x) = 42 x^{2} + 12

= (6 x + 19) (14 x^{3} + 12 x) + (42 x^{2} + 12) (3 x^{2} + 19 x - 7)

Simplify

(6 x + 19) (14 x^{3} + 12 x) + (42 x^{2} + 12) (3 x^{2} + 19 x - 7) : 210 x^{4} + 1064 x^{3} - 186 x^{2} + 456 x - 84

= 210 x^{4} + 1064 x^{3} - 186 x^{2} + 456 x - 84

x \to 0 lim (\frac{1}{x - 2})

x^{2} y^{^{'}} - x y - x^{3} sin (x) = 0

\frac{d}{d x} (\frac{3 π}{4 x ^{5}})

\int \frac{12}{1 - cos ( 6 x )} d x

x^{3} + y^{3} = 126

What is the derivative of (3x^2+19x-7(14x^3+12x)) ?
The derivative of (3x^2+19x-7(14x^3+12x)) is 210x^4+1064x^3-186x^2+456x-84
What is the first derivative of (3x^2+19x-7(14x^3+12x)) ?
The first derivative of (3x^2+19x-7(14x^3+12x)) is 210x^4+1064x^3-186x^2+456x-84