Question

Question #24991

Answer 1

`(dy)/(dx) = -a^(1/2) log(a) sinx`

Explanation:

For this circumstance `a` is simply a constant...

Hence `a^(1/2)*log(a)` is also simply a constant

We must use our knowledge of trigonometric differentiation...

`d/(dx) ( ksinnx ) = k*ncosnx`

`d/(dx) ( kcosnx) = k*n*-sinnx = -knsinnx`

`therefore d/(dx) ( a^(1/2) log(a) cosx ) = a^(1/2)log(a) * -sinx`

`=> (dy)/(dx) = -a^(1/2)log(a)sinx`