Solve f(x)= ((x-2)(x-4))/ ((x-3)(x a) )

Evaluate

f (x) = \frac{( x - 2 ) ( x - 4 )}{( x - 3 ) x a}

Simplify

f (x) = \frac{( x - 2 ) ( x - 4 )}{x a ( x - 3 )}

Evaluate

f (x) = \frac{( x - 2 ) ( x - 4 )}{a x ( x - 3 )}

Take the derivative of both sides

f^{'} (x) = \frac{d}{d x} (\frac{( x - 2 ) ( x - 4 )}{a x ( x - 3 )})

Calculate

f^{'} (x) = \frac{d}{d x} (\frac{x ^{2} - 6 x + 8}{a x ^{2} - 3 a x})

Use differentiation rule \frac{d}{d x} (\frac{f ( x )}{g ( x )}) = \frac{\frac{d}{d x} ( f ( x )) \times g ( x ) - f ( x ) \times \frac{d}{d x} ( g ( x ) )}{( g ( x ) ) ^{2}}

f^{'} (x) = \frac{\frac{d}{d x} ( x ^{2} - 6 x + 8 ) \times ( a x ^{2} - 3 a x ) - ( x ^{2} - 6 x + 8 ) \times \frac{d}{d x} ( a x ^{2} - 3 a x )}{( a x ^{2} - 3 a x ) ^{2}}

Calculate

More Steps

f^{'} (x) = \frac{( 2 x - 6 ) ( a x ^{2} - 3 a x ) - ( x ^{2} - 6 x + 8 ) \times \frac{d}{d x} ( a x ^{2} - 3 a x )}{( a x ^{2} - 3 a x ) ^{2}}

Calculate

More Steps

f^{'} (x) = \frac{( 2 x - 6 ) ( a x ^{2} - 3 a x ) - ( x ^{2} - 6 x + 8 ) ( 2 a x - 3 a )}{( a x ^{2} - 3 a x ) ^{2}}

Subtract the terms

More Steps

f^{'} (x) = \frac{3 a x ^{2} - 16 a x + 24 a}{( a x ^{2} - 3 a x ) ^{2}}

Solution

More Steps

f^{'} (x) = \frac{3 x ^{2} - 16 x + 24}{a ( x ^{2} - 3 x ) ^{2}}

Function