SOLUTION: Find {{{ dy/dx }}} (Does not need to simplifited, just show the first step) (a). {{{ y=tan^3(e^(5x)) }}} (b). {{{ y=2^(6x-5) }}} (c). {{{ y=(x^2+sqrt(x))/(cos(x)) }}} (d). {{

Algebra ->  Equations -> SOLUTION: Find {{{ dy/dx }}} (Does not need to simplifited, just show the first step) (a). {{{ y=tan^3(e^(5x)) }}} (b). {{{ y=2^(6x-5) }}} (c). {{{ y=(x^2+sqrt(x))/(cos(x)) }}} (d). {{      Log On


   

Question 991362: Find +dy%2Fdx+ (Does not need to simplifited, just show the first step)
(a). +y=tan%5E3%28e%5E%285x%29%29+
(b). +y=2%5E%286x-5%29+
(c). +y=%28x%5E2%2Bsqrt%28x%29%29%2F%28cos%28x%29%29+
(d). +y=x%5E2ln%285x%29+

Please give details
Thank you
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
(a). +y=tan%5E3%28e%5E%285x%29%29+

Many times apply the chain rule for a derivative:

dy%2Fdx = . . . . . . . . . . . . . . . . . . . (use the formula   %28d%2Fdx%29%28x%5E3%29 = 3x%5E2  first;   it gives)

= 3tan%5E2%28e%5E%285x%29%29%2A%28d%2Fdx%29+%28tan%28e%5E%285x%29%29%29+ = . . . . (then use the formula %28d%2Fdx%29%28tan%28x%29%29 = 1%2Fcos%5E2%28x%29;   it gives)

= 3tan%5E2%28e%5E%285x%29%29*1%2Fcos%5E2%28e%5E%285x%29%29%29*%28d%2Fdx%29+%28e%5E%285x%29%29 =

= 3tan%5E2%28e%5E%285x%29%29*1%2Fcos%5E2%28e%5E%285x%29%29%29*5%2Ae%5E%285x%29.