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

The derivative of 4xsqrt(3x^2+2) is (4(6x^2+2))/(sqrt(3x^2+2))

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

The first derivative of 4xsqrt(3x^2+2) is (4(6x^2+2))/(sqrt(3x^2+2))

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derivative of

4 x 3 x^{2} + 2

\frac{4 ( 6 x ^{2} + 2 )}{3 x ^{2} + 2}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

= 4 (1 \cdot 3 x^{2} + 2 + \frac{3 x}{3 x ^{2} + 2} x)

Simplify

4 (1 \cdot 3 x^{2} + 2 + \frac{3 x}{3 x ^{2} + 2} x) : \frac{4 ( 6 x ^{2} + 2 )}{3 x ^{2} + 2}

= \frac{4 ( 6 x ^{2} + 2 )}{3 x ^{2} + 2}

\frac{x ^{5}}{10} + \frac{1}{6 x ^{3}}

t \cdot \frac{d y}{d t} = t^{3} + 14 t^{3} y

\int \frac{cos ( t )}{sin ^{4} ( t ) - 16} d t

\frac{d}{d x} (\frac{x + 5}{x + 1})

x \to 1 lim (\frac{4 - x ^{2}}{x + 2})

What is the derivative of 4xsqrt(3x^2+2) ?
The derivative of 4xsqrt(3x^2+2) is (4(6x^2+2))/(sqrt(3x^2+2))
What is the first derivative of 4xsqrt(3x^2+2) ?
The first derivative of 4xsqrt(3x^2+2) is (4(6x^2+2))/(sqrt(3x^2+2))