Question

hy..!!
solve question no.3 part 1
class 12th
maths
differentiation
thanks​

Answer 1

Answer:

Step-by-step explanation:

using product rule and chain rule ( applying it directly as expected from grade 12 students)

eᵃˣcos(bx+c) = (eᵃˣ)'cos(bx+c) + eᵃˣ(cos{bx+c})'

                    = aeᵃˣcos(bx+c) - b.eᵃˣsin(bx+c)

                    = eᵃˣ(acos(bx+c) - bsin(bx+c))

Answer 2

hay mate I m answering your question please comment me if you like my answer
by applying Leibnitz rule 
$\frac{d {}^{n} }{dx {}^{n} } (e {}^{ax} cos(bx + c) = ∑ _{k = 0} ^{n } \binom{n}{k} \frac{d ^{k} }{dx^{k} } (e^{ax} ) \frac{d ^{n - k} }{dx {}^{n - k} } (cos(bx + c)) = ∑ _{k = 0} ^{n} \binom{n}{k} a^{k} e {}^{ax} b {}^{n - k} cos(bx + c \frac{n\pi}{2}$
Just evaluate this finite sum term wise and you are free from the burden of repeated application of derivatives.