What is the derivative of 5/((f^2(x)-f(x)+2)) ?

The derivative of 5/((f^2(x)-f(x)+2)) is -(5(2fx-x))/((f^2x-fx+2)^2)

What is the first derivative of 5/((f^2(x)-f(x)+2)) ?

The first derivative of 5/((f^2(x)-f(x)+2)) is -(5(2fx-x))/((f^2x-fx+2)^2)

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derivative of

\frac{5}{( f ^{2} ( x ) - f ( x ) + 2 )}

- \frac{5 ( 2 f x - x )}{( f ^{2} x - f x + 2 ) ^{2}}

Solution steps

\frac{d}{df} (\frac{5}{f ^{2} x - f x + 2})

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{5 ( 2 f x - x )}{( f ^{2} x - f x + 2 ) ^{2}}

\frac{d}{d t} (2 + 1 t + 5 t^{2})

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

x^{3} - x - 1

cos^{4} (\frac{x}{2}) - sin^{4} (\frac{x}{2})

\frac{- x ^{3} + x - 1}{2}

What is the derivative of 5/((f^2(x)-f(x)+2)) ?
The derivative of 5/((f^2(x)-f(x)+2)) is -(5(2fx-x))/((f^2x-fx+2)^2)
What is the first derivative of 5/((f^2(x)-f(x)+2)) ?
The first derivative of 5/((f^2(x)-f(x)+2)) is -(5(2fx-x))/((f^2x-fx+2)^2)