derivative of y = e^((k)tan(sqrt(3x)))

Question

derivative of y = e^((k)tan(sqrt(3x)))

Answer 1

y = e^((k)tan(sqrt(3x))) y = e^{ktan(sqrt(3x))}

written with a minimum # of parentheses.

 

y'=e^{ktan(sqrt(3x))}•ksec²(√(3x))•½•√3(1/√x)

and you get to simplify it (& check it)!

 

Basically deriv. of exponential is exponential, with further factors obtained by differentiating exponent, which involves a succession of chain rule applications.

deriv. of sqrt of 3x has constant factor 3^½, then deriv. of sqrt of x^½