What is the derivative of 1/3 xsqrt(x^2+5) ?

The derivative of 1/3 xsqrt(x^2+5) is (2x^2+5)/(3sqrt(x^2+5))

What is the first derivative of 1/3 xsqrt(x^2+5) ?

The first derivative of 1/3 xsqrt(x^2+5) is (2x^2+5)/(3sqrt(x^2+5))

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\frac{d}{d x} (\frac{1}{3} x x^{2} + 5)

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

Solution steps

\frac{d}{d x} (\frac{1}{3} x x^{2} + 5)

Take the constant out:

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

= \frac{1}{3} \frac{d}{d x} (x x^{2} + 5)

Apply the Product Rule:

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

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

= \frac{1}{3} (\frac{d x}{d x} x^{2} + 5 + \frac{d}{d x} (x^{2} + 5) x)

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

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

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

Simplify

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

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

\int \frac{1}{- 4 t ^{2} + 12 t + 7} d t

\int_{0}^{π} sin (x^{2}) d x

\int cos (t) + sin^{3} (t) d t

y^{^{'}} + \frac{6}{x ^{2}} y = x^{10} e^{\frac{6}{x}}

\int (x - 4) (x + 4) d x

What is the derivative of 1/3 xsqrt(x^2+5) ?
The derivative of 1/3 xsqrt(x^2+5) is (2x^2+5)/(3sqrt(x^2+5))
What is the first derivative of 1/3 xsqrt(x^2+5) ?
The first derivative of 1/3 xsqrt(x^2+5) is (2x^2+5)/(3sqrt(x^2+5))