What is the derivative of ((x-3/(x+4))(x^2+2x+1)) ?

The derivative of ((x-3/(x+4))(x^2+2x+1)) is (2x^3+11x^2-8x-17)/((x+4)^2)

What is the first derivative of ((x-3/(x+4))(x^2+2x+1)) ?

The first derivative of ((x-3/(x+4))(x^2+2x+1)) is (2x^3+11x^2-8x-17)/((x+4)^2)

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\frac{d}{d x} ((\frac{x - 3}{x + 4}) (x^{2} + 2 x + 1))

\frac{2 x ^{3} + 11 x ^{2} - 8 x - 17}{( x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} ((\frac{x - 3}{x + 4}) (x^{2} + 2 x + 1))

Apply the Product Rule:

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

f = \frac{x - 3}{x + 4}, g = x^{2} + 2 x + 1

= \frac{d}{d x} (\frac{x - 3}{x + 4}) (x^{2} + 2 x + 1) + \frac{d}{d x} (x^{2} + 2 x + 1) \frac{x - 3}{x + 4}

\frac{d}{d x} (\frac{x - 3}{x + 4}) = \frac{7}{( x + 4 ) ^{2}}

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

= \frac{7}{( x + 4 ) ^{2}} (x^{2} + 2 x + 1) + (2 x + 2) \frac{x - 3}{x + 4}

Simplify

\frac{7}{( x + 4 ) ^{2}} (x^{2} + 2 x + 1) + (2 x + 2) \frac{x - 3}{x + 4} : \frac{2 x ^{3} + 11 x ^{2} - 8 x - 17}{( x + 4 ) ^{2}}

= \frac{2 x ^{3} + 11 x ^{2} - 8 x - 17}{( x + 4 ) ^{2}}

\int_{0}^{3} sin^{2} (m x) d x

\frac{1}{6 x - 12} 2 x + 16

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

\frac{\partial}{\partial x} (x^{2} + y^{3})

h (x) = 3 e^{x} - 7 x, (0, 3)

What is the derivative of ((x-3/(x+4))(x^2+2x+1)) ?
The derivative of ((x-3/(x+4))(x^2+2x+1)) is (2x^3+11x^2-8x-17)/((x+4)^2)
What is the first derivative of ((x-3/(x+4))(x^2+2x+1)) ?
The first derivative of ((x-3/(x+4))(x^2+2x+1)) is (2x^3+11x^2-8x-17)/((x+4)^2)