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Popular >

derivative of sqrt(3x^2+5x+8)

Solution

\frac{d}{d x} (3 x^{2} + 5 x + 8)

Solution

\frac{6 x + 5}{2 3 x ^{2} + 5 x + 8}

Solution steps

\frac{d}{d x} (3 x^{2} + 5 x + 8)

Apply the chain rule:

\frac{1}{2 3 x ^{2} + 5 x + 8} \frac{d}{d x} (3 x^{2} + 5 x + 8)

= \frac{1}{2 3 x ^{2} + 5 x + 8} \frac{d}{d x} (3 x^{2} + 5 x + 8)

\frac{d}{d x} (3 x^{2} + 5 x + 8) = 6 x + 5

= \frac{1}{2 3 x ^{2} + 5 x + 8} (6 x + 5)

Simplify

\frac{1}{2 3 x ^{2} + 5 x + 8} (6 x + 5) : \frac{6 x + 5}{2 3 x ^{2} + 5 x + 8}

= \frac{6 x + 5}{2 3 x ^{2} + 5 x + 8}

Popular Examples

integral of cos(6t)

\int cos (6 t) d t

area 4sqrt(2x),2x^2,-4x+6 area

4 2 x, 2 x^{2}, - 4 x + 6

(t+2)y'+y= 1/(t-1)

(t + 2) y^{'} + y = \frac{1}{t - 1}

(\partial)/(\partial l)(2pisqrt(l/({g))})

\frac{\partial}{\partial l} (2 π \frac{l}{g})

16y^{''}-pi^2y=0

16 y^{^{''}} - π^{2} y = 0

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(3x^2+5x+8) ?
The derivative of sqrt(3x^2+5x+8) is (6x+5)/(2sqrt(3x^2+5x+8))
What is the first derivative of sqrt(3x^2+5x+8) ?
The first derivative of sqrt(3x^2+5x+8) is (6x+5)/(2sqrt(3x^2+5x+8))