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

The derivative of 2x(3x^2-7^3) is 2((3x^2-7)^3+18x^2(3x^2-7)^2)

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

The first derivative of 2x(3x^2-7^3) is 2((3x^2-7)^3+18x^2(3x^2-7)^2)

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

2 ((3 x^{2} - 7)^{3} + 18 x^{2} (3 x^{2} - 7)^{2})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = (3 x^{2} - 7)^{3}

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((3 x^{2} - 7)^{3}) = 18 x (3 x^{2} - 7)^{2}

= 2 (1 \cdot (3 x^{2} - 7)^{3} + 18 x (3 x^{2} - 7)^{2} x)

Simplify

2 (1 \cdot (3 x^{2} - 7)^{3} + 18 x (3 x^{2} - 7)^{2} x) : 2 ((3 x^{2} - 7)^{3} + 18 x^{2} (3 x^{2} - 7)^{2})

= 2 ((3 x^{2} - 7)^{3} + 18 x^{2} (3 x^{2} - 7)^{2})

x \to 3 lim (\frac{x ^{2} - 1}{x - 3})

\int \frac{z}{z - 1} d z

\int \frac{2}{x ^{2} - x} d x

\frac{d v}{d t}

(x + y)^{2} d x + (2 x y + x^{2} - 3) d y = 0

What is the derivative of 2x(3x^2-7^3) ?
The derivative of 2x(3x^2-7^3) is 2((3x^2-7)^3+18x^2(3x^2-7)^2)
What is the first derivative of 2x(3x^2-7^3) ?
The first derivative of 2x(3x^2-7^3) is 2((3x^2-7)^3+18x^2(3x^2-7)^2)