Question
Function
f′(x)=abln(c)×cbx
Evaluate
f(x)=cxba
Simplify
f(x)=acxb
Evaluate
f(x)=acbx
Take the derivative of both sides
f′(x)=dxd(acbx)
Simplify
f′(x)=a×dxd(cbx)
Solution
More Steps

Evaluate
dxd(cbx)
Use the chain rule dxd(f(g))=dgd(f(g))×dxd(g) where the g=bx, to find the derivative
dgd(cg)×dxd(bx)
Use dxdax=ln(a)ax to find derivative
ln(c)×cg×dxd(bx)
Calculate
ln(c)×cgb
Substitute back
ln(c)×cbxb
Use the commutative property to reorder the terms
ln(c)×bcbx
Simplify
bln(c)×cbx
f′(x)=abln(c)×cbx
Show Solution
