What is the derivative of 3x^{-3}(x^4-3x^3+10x-9) ?

The derivative of 3x^{-3}(x^4-3x^3+10x-9) is (3(x^4-20x+27))/(x^4)

What is the first derivative of 3x^{-3}(x^4-3x^3+10x-9) ?

The first derivative of 3x^{-3}(x^4-3x^3+10x-9) is (3(x^4-20x+27))/(x^4)

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derivative of

3 x^{- 3} (x^{4} - 3 x^{3} + 10 x - 9)

\frac{3 ( x ^{4} - 20 x + 27 )}{x ^{4}}

Solution steps

\frac{d}{d x} (3 x^{- 3} (x^{4} - 3 x^{3} + 10 x - 9))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (x^{- 3} (x^{4} - 3 x^{3} + 10 x - 9))

Apply the Product Rule:

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

f = x^{- 3}, g = x^{4} - 3 x^{3} + 10 x - 9

= 3 (\frac{d}{d x} (x^{- 3}) (x^{4} - 3 x^{3} + 10 x - 9) + \frac{d}{d x} (x^{4} - 3 x^{3} + 10 x - 9) x^{- 3})

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

\frac{d}{d x} (x^{4} - 3 x^{3} + 10 x - 9) = 4 x^{3} - 9 x^{2} + 10

= 3 ((- \frac{3}{x ^{4}}) (x^{4} - 3 x^{3} + 10 x - 9) + (4 x^{3} - 9 x^{2} + 10) x^{- 3})

Simplify

3 ((- \frac{3}{x ^{4}}) (x^{4} - 3 x^{3} + 10 x - 9) + (4 x^{3} - 9 x^{2} + 10) x^{- 3}) : \frac{3 ( x ^{4} - 20 x + 27 )}{x ^{4}}

= \frac{3 ( x ^{4} - 20 x + 27 )}{x ^{4}}

\int \frac{1}{x ^{2} + z ^{2}} d x

\int \frac{9 e ^{x}}{e ^{x} - 1} d x

\frac{\partial}{\partial x} (x^{4} + 5 x^{2} y)

y^{^{''}} - 7 y^{^{'}} + 10 y = 0

\int \frac{4}{x ( ln ( x ) ) ^{2}} d x

What is the derivative of 3x^{-3}(x^4-3x^3+10x-9) ?
The derivative of 3x^{-3}(x^4-3x^3+10x-9) is (3(x^4-20x+27))/(x^4)
What is the first derivative of 3x^{-3}(x^4-3x^3+10x-9) ?
The first derivative of 3x^{-3}(x^4-3x^3+10x-9) is (3(x^4-20x+27))/(x^4)