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

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Type your math problem... f(x)= (x-2)(x-4)/(x-3)(x a)

Question

Function

f^{'} (x) = \frac{2 a x ^{3} - 15 a x ^{2} + 36 a x - 24 a}{( x - 3 ) ^{2}}

Evaluate

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

Simplify

More Steps

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

Evaluate

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

Take the derivative of both sides

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

Calculate

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

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

Calculate

More Steps

f^{'} (x) = \frac{( 3 a x ^{2} - 12 a x + 8 a ) ( x - 3 ) - ( a x ^{3} - 6 a x ^{2} + 8 a x ) \times \frac{d}{d x} ( x - 3 )}{( x - 3 ) ^{2}}

Calculate

More Steps

f^{'} (x) = \frac{( 3 a x ^{2} - 12 a x + 8 a ) ( x - 3 ) - ( a x ^{3} - 6 a x ^{2} + 8 a x ) \times 1}{( x - 3 ) ^{2}}

Any expression multiplied by 1 remains the same

f^{'} (x) = \frac{( 3 a x ^{2} - 12 a x + 8 a ) ( x - 3 ) - ( a x ^{3} - 6 a x ^{2} + 8 a x )}{( x - 3 ) ^{2}}

Solution

More Steps

f^{'} (x) = \frac{2 a x ^{3} - 15 a x ^{2} + 36 a x - 24 a}{( x - 3 ) ^{2}}

Show Solution