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

The derivative of x*sqrt(3x^2+5) is (6x^2+5)/(sqrt(3x^2+5))

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

The first derivative of x*sqrt(3x^2+5) is (6x^2+5)/(sqrt(3x^2+5))

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derivative of

x \cdot 3 x^{2} + 5

\frac{6 x ^{2} + 5}{3 x ^{2} + 5}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot 3 x^{2} + 5 + \frac{3 x}{3 x ^{2} + 5} x

Simplify

1 \cdot 3 x^{2} + 5 + \frac{3 x}{3 x ^{2} + 5} x : \frac{6 x ^{2} + 5}{3 x ^{2} + 5}

= \frac{6 x ^{2} + 5}{3 x ^{2} + 5}

x^{2}, x, - 1, 1

x^{2} - 2, x, - 2, 2

y^{^{'}} = \frac{4 x y}{2 + x ^{2}}

x \to - 4 lim (- x^{2} + 4 x - 9)

y^{^{''}} - 3 y^{^{'}} = t^{3} - 6

What is the derivative of x*sqrt(3x^2+5) ?
The derivative of x*sqrt(3x^2+5) is (6x^2+5)/(sqrt(3x^2+5))
What is the first derivative of x*sqrt(3x^2+5) ?
The first derivative of x*sqrt(3x^2+5) is (6x^2+5)/(sqrt(3x^2+5))