Question #31152

1 Answer
Bobert
Oct 19, 2017

#dy/dx=tan(x)#

Explanation:

Take the derivative of each term. The derivative of #4# is zero, since it is a constant. To take the derivative of #ln(sec(x))#, we must use the chain rule, multiplying by the derivative of the outside by the derivative of the inside like so:

#dy/dx=1/sec(x)*d/dx(sec(x))#

Evaluate the the derivative of #sec(x)#.

#dy/dx=1/sec(x)*sec(x)tan(x)#

Simplify:

#dy/dx=1/cancelsec(x)*cancelsec(x)tan(x)#

#dy/dx=tan(x)#

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