What is the derivative of 1/((x^5-x+1^9)) ?

The derivative of 1/((x^5-x+1^9)) is -(9(5x^4-1))/((x^5-x+1)^{10)}

What is the first derivative of 1/((x^5-x+1^9)) ?

The first derivative of 1/((x^5-x+1^9)) is -(9(5x^4-1))/((x^5-x+1)^{10)}

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\frac{d}{d x} (\frac{1}{( x ^{5} - x + 1 ) ^{9}})

- \frac{9 ( 5 x ^{4} - 1 )}{( x ^{5} - x + 1 ) ^{10}}

Solution steps

\frac{d}{d x} (\frac{1}{( x ^{5} - x + 1 ) ^{9}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x^{5} - x + 1)^{- 9})

Apply the chain rule:

- \frac{9}{( x ^{5} - x + 1 ) ^{10}} \frac{d}{d x} (x^{5} - x + 1)

= - \frac{9}{( x ^{5} - x + 1 ) ^{10}} \frac{d}{d x} (x^{5} - x + 1)

\frac{d}{d x} (x^{5} - x + 1) = 5 x^{4} - 1

= - \frac{9}{( x ^{5} - x + 1 ) ^{10}} (5 x^{4} - 1)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{9 ( 5 x ^{4} - 1 )}{( x ^{5} - x + 1 ) ^{10}}

y^{^{''}} - 26 y^{^{'}} + 169 y = 0

\int 10 x + 11 x d x

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

\int \frac{3 x}{1 - x ^{2}} d x

x (x - 6)^{2}

What is the derivative of 1/((x^5-x+1^9)) ?
The derivative of 1/((x^5-x+1^9)) is -(9(5x^4-1))/((x^5-x+1)^{10)}
What is the first derivative of 1/((x^5-x+1^9)) ?
The first derivative of 1/((x^5-x+1^9)) is -(9(5x^4-1))/((x^5-x+1)^{10)}