What is the derivative of (2x+1^2sqrt(3(2x+1)+10)) ?

The derivative of (2x+1^2sqrt(3(2x+1)+10)) is (60x^2+140x+55)/(sqrt(6x+13))

What is the first derivative of (2x+1^2sqrt(3(2x+1)+10)) ?

The first derivative of (2x+1^2sqrt(3(2x+1)+10)) is (60x^2+140x+55)/(sqrt(6x+13))

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\frac{d}{d x} ((2 x + 1)^{2} 3 (2 x + 1) + 10)

\frac{60 x ^{2} + 140 x + 55}{6 x + 13}

Solution steps

\frac{d}{d x} ((2 x + 1)^{2} 3 (2 x + 1) + 10)

Simplify

(2 x + 1)^{2} 3 (2 x + 1) + 10 : (2 x + 1)^{2} 6 x + 13

= \frac{d}{d x} ((2 x + 1)^{2} 6 x + 13)

Apply the Product Rule:

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

f = (2 x + 1)^{2}, g = 6 x + 13

= \frac{d}{d x} ((2 x + 1)^{2}) 6 x + 13 + \frac{d}{d x} (6 x + 13) (2 x + 1)^{2}

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

\frac{d}{d x} (6 x + 13) = \frac{3}{6 x + 13}

= 4 (2 x + 1) 6 x + 13 + \frac{3}{6 x + 13} (2 x + 1)^{2}

Simplify

4 (2 x + 1) 6 x + 13 + \frac{3}{6 x + 13} (2 x + 1)^{2} : \frac{60 x ^{2} + 140 x + 55}{6 x + 13}

= \frac{60 x ^{2} + 140 x + 55}{6 x + 13}

\frac{1}{s ^{2} - s + 1}

n = 0 \sum \infty 7 (\frac{2}{3})^{n}

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

x \to 3 lim (\frac{x + 3}{x + 2})

\frac{d}{d x} (\frac{7}{8 x ^{5}})

What is the derivative of (2x+1^2sqrt(3(2x+1)+10)) ?
The derivative of (2x+1^2sqrt(3(2x+1)+10)) is (60x^2+140x+55)/(sqrt(6x+13))
What is the first derivative of (2x+1^2sqrt(3(2x+1)+10)) ?
The first derivative of (2x+1^2sqrt(3(2x+1)+10)) is (60x^2+140x+55)/(sqrt(6x+13))