Differentiate the following with respect to x by first principles: 3 cos (4x) − 5 sin (4x)

Question

anonymous · Answer

$$f(x)\prime=\lim_{h \rightarrow 0} \frac{ f(x+h) -f(x)}{ h }$$

anonymous · Answer

@reemii

reemii · Answer

do you have to use this limit ?

reemii · Answer

what do you call "first principles' ?

anonymous · Answer

that's first principles formula (limit)

anonymous · Answer

we have to get rid of h at the denominator, then replace h with zero

reemii · Answer

you probably probably have somewhere in your course the proof, with this limit, that
$(\sin(x))'=\cos( x)$. You should take this and use this as base for this question.

amistre64 · Answer

you will need to remember your trig(a+b) identities

amistre64 · Answer

3 cos (4(x+h)) − 5 sin (4(x+h))

3 cos (4x+4h) − 5 sin (4x+4h)

3(cos(4x)cos(4h)-sin(4x)sin(4h)) - 5(sin(4x)cos(4h)+sin(4h)cos(4x))

.... etc

amistre64 · Answer

and yes, recalling the sinh/h and cosh/h  limits from squeeze thrm would have to be applied