### Video Transcript

If π¦ equals seven tan two π₯, find
ππ¦ ππ₯.

In order to actually solve this
problem and differentiate π¦ equals seven tan two π₯, we need to know a couple of
sets of general rules. So the first one is that if π¦ is
equal to tan π₯, then we know that ππ¦ ππ₯ β so our derivative β is gonna be equal
to sec squared π₯. However, if we take a look at our
function, okay, yes, weβve got π¦ is equal to tan π₯. But itβs not that simple because
weβve got π¦ is equal to seven tan two π₯.

So therefore, what we can actually
say is that our function is more in this form π¦ equals π tan π π₯. So what itβs saying is weβve got a
constant π which is our seven and then tan of a function and our function is two
π₯. Well, we can say that if itβs in
this form, then ππ¦ ππ₯ β so our derivative β is gonna be equal to π multiplied
by the derivative of our function π π₯ multiplied by sec squared π π₯ β so our
function π₯.

Okay, so great, we now have
this. Letβs use it to actually
differentiate our function and find ππ¦ ππ₯. Okay, so we have π¦ equals seven
tan two π₯. Well, using our rule, we can
actually say that ππ¦ ππ₯ is gonna be equal to seven multiplied by the derivative
of two π₯ multiplied by sec squared two π₯.

Well, if we differentiate two π₯ with
respect to π₯, what weβre gonna get is two multiplied by one because itβs our
coefficient multiplied by our exponent then π₯ to the power of one minus one which
is gonna be equal to two π₯ to the power of zero. Well, we know that anything to the
power of zero is one. So therefore, this is just gonna
give us a result of two.

Okay, so letβs put this back
in. So weβre gonna get that ππ¦ ππ₯
is equal to seven multiplied by two multiplied by sec squared two π₯.

So therefore, we can say that if π¦
equals seven tan two π₯, then ππ¦ ππ₯ is gonna be equal to 14 sec squared two
π₯.