What is the derivative of 7/(x^8+5x+1) ?

The derivative of 7/(x^8+5x+1) is -(7(8x^7+5))/((x^8+5x+1)^2)

What is the first derivative of 7/(x^8+5x+1) ?

The first derivative of 7/(x^8+5x+1) is -(7(8x^7+5))/((x^8+5x+1)^2)

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\frac{d}{d x} (\frac{7}{x ^{8} + 5 x + 1})

- \frac{7 ( 8 x ^{7} + 5 )}{( x ^{8} + 5 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7}{x ^{8} + 5 x + 1})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{1}{x ^{8} + 5 x + 1})

Apply exponent rule:

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

= 7 \frac{d}{d x} ((x^{8} + 5 x + 1)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{8} + 5 x + 1 ) ^{2}} \frac{d}{d x} (x^{8} + 5 x + 1)

= - \frac{1}{( x ^{8} + 5 x + 1 ) ^{2}} \frac{d}{d x} (x^{8} + 5 x + 1)

\frac{d}{d x} (x^{8} + 5 x + 1) = 8 x^{7} + 5

= 7 (- \frac{1}{( x ^{8} + 5 x + 1 ) ^{2}} (8 x^{7} + 5))

Simplify

7 (- \frac{1}{( x ^{8} + 5 x + 1 ) ^{2}} (8 x^{7} + 5)) : - \frac{7 ( 8 x ^{7} + 5 )}{( x ^{8} + 5 x + 1 ) ^{2}}

= - \frac{7 ( 8 x ^{7} + 5 )}{( x ^{8} + 5 x + 1 ) ^{2}}

\frac{d}{d x} (sin (14 x))

y^{^{'}} = 1 + y^{2} + x + x y^{2}

\int \frac{( 1 + x )}{x} d x

x \to 0 lim (2 x + 12)

ln (sec^{2} (x))

What is the derivative of 7/(x^8+5x+1) ?
The derivative of 7/(x^8+5x+1) is -(7(8x^7+5))/((x^8+5x+1)^2)
What is the first derivative of 7/(x^8+5x+1) ?
The first derivative of 7/(x^8+5x+1) is -(7(8x^7+5))/((x^8+5x+1)^2)