What is the derivative of (x^2-2x+1(1-3x^{-5})) ?

The derivative of (x^2-2x+1(1-3x^{-5})) is (2x^7+9x^2-24x+15)/(x^6)-2

What is the first derivative of (x^2-2x+1(1-3x^{-5})) ?

The first derivative of (x^2-2x+1(1-3x^{-5})) is (2x^7+9x^2-24x+15)/(x^6)-2

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

\frac{2 x ^{7} + 9 x ^{2} - 24 x + 15}{x ^{6}} - 2

Solution steps

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

Apply the Product Rule:

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

f = x^{2} - 2 x + 1, g = 1 - 3 x^{- 5}

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

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

\frac{d}{d x} (1 - 3 x^{- 5}) = \frac{15}{x ^{6}}

= (2 x - 2) (1 - 3 x^{- 5}) + \frac{15}{x ^{6}} (x^{2} - 2 x + 1)

Simplify

(2 x - 2) (1 - 3 x^{- 5}) + \frac{15}{x ^{6}} (x^{2} - 2 x + 1) : \frac{2 x ^{7} + 9 x ^{2} - 24 x + 15}{x ^{6}} - 2

= \frac{2 x ^{7} + 9 x ^{2} - 24 x + 15}{x ^{6}} - 2

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

F (x) = (7 x^{6} + 2 x^{3})^{4}

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

\int \frac{1}{81 e ^{- 8 x} + e ^{8 x}} d x

\frac{d}{d x} (cos (sin (2 x + 5)))

What is the derivative of (x^2-2x+1(1-3x^{-5})) ?
The derivative of (x^2-2x+1(1-3x^{-5})) is (2x^7+9x^2-24x+15)/(x^6)-2
What is the first derivative of (x^2-2x+1(1-3x^{-5})) ?
The first derivative of (x^2-2x+1(1-3x^{-5})) is (2x^7+9x^2-24x+15)/(x^6)-2