Solve f(x)=loga(x b)

Evaluate

f (x) = lo g_{10} (a) \times x b

Simplify

f (x) = x b lo g_{10} (a)

Evaluate

f (x) = b x lo g_{10} (a)

Take the derivative of both sides

f^{'} (x) = \frac{d}{d x} (b x lo g_{10} (a))

Use differentiation rule \frac{d}{d x} (f (x) \times g (x)) = \frac{d}{d x} (f (x)) \times g (x) + f (x) \times \frac{d}{d x} (g (x))

f^{'} (x) = \frac{d}{d x} (b x) \times lo g_{10} (a) + b x \times \frac{d}{d x} (lo g_{10} (a))

Calculate

More Steps

f^{'} (x) = b lo g_{10} (a) + b x \times \frac{d}{d x} (lo g_{10} (a))

Use \frac{d}{d x} (c) = 0 to find derivative

f^{'} (x) = b lo g_{10} (a) + b x \times 0

Calculate

f^{'} (x) = b lo g_{10} (a) + 0

Solution

f^{'} (x) = b lo g_{10} (a)

Function