What is the derivative of sqrt(x+1)(16+8x+9x^2) ?

The derivative of sqrt(x+1)(16+8x+9x^2) is (45x^2+60x+32)/(2sqrt(x+1))

What is the first derivative of sqrt(x+1)(16+8x+9x^2) ?

The first derivative of sqrt(x+1)(16+8x+9x^2) is (45x^2+60x+32)/(2sqrt(x+1))

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\frac{d}{d x} (x + 1 (16 + 8 x + 9 x^{2}))

\frac{45 x ^{2} + 60 x + 32}{2 x + 1}

Solution steps

\frac{d}{d x} (x + 1 (16 + 8 x + 9 x^{2}))

Apply the Product Rule:

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

f = x + 1, g = 16 + 8 x + 9 x^{2}

= \frac{d}{d x} (x + 1) (16 + 8 x + 9 x^{2}) + \frac{d}{d x} (16 + 8 x + 9 x^{2}) x + 1

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

\frac{d}{d x} (16 + 8 x + 9 x^{2}) = 18 x + 8

= \frac{1}{2 x + 1} (16 + 8 x + 9 x^{2}) + (18 x + 8) x + 1

Simplify

\frac{1}{2 x + 1} (16 + 8 x + 9 x^{2}) + (18 x + 8) x + 1 : \frac{45 x ^{2} + 60 x + 32}{2 x + 1}

= \frac{45 x ^{2} + 60 x + 32}{2 x + 1}

x y^{^{'}} + y = y^{2}, y (1) = - 7

\int \frac{169}{x ^{3} - 13 x ^{2}} d x

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

\frac{d}{d x} ((x^{3} + 4 x)^{(x^{5} + 3 x^{2})})

What is the derivative of sqrt(x+1)(16+8x+9x^2) ?
The derivative of sqrt(x+1)(16+8x+9x^2) is (45x^2+60x+32)/(2sqrt(x+1))
What is the first derivative of sqrt(x+1)(16+8x+9x^2) ?
The first derivative of sqrt(x+1)(16+8x+9x^2) is (45x^2+60x+32)/(2sqrt(x+1))