# How do you differentiate f(x)=sqrtcos(7-4x)  using the chain rule?

Mar 30, 2016

f'(x)=(4sin(7-4x))/(2sqrt(cos(7-4x))
$f \left(x\right) = \sqrt{\cos \left(7 - 4 x\right)}$
$f \left(x\right) = {\left(\cos \left(7 - 4 x\right)\right)}^{\frac{1}{2}}$
$f ' \left(x\right) = \frac{1}{2} {\left(\cos \left(7 - 4 x\right)\right)}^{- \frac{1}{2}} \cdot - \sin \left(7 - 4 x\right) \cdot - 4$
f'(x)=(4sin(7-4x))/(2sqrt(cos(7-4x))