# Differentiation Questions

Solution : Since by deleting a single term from an infinite series, it remains same. Therefore, the given function may be written as y = $$\sqrt{sin x + y}$$ Squaring on both sides, $$\implies$$  $$y^2$$  = sin x + y By using differentiation of infinite series, Differentiating both sides with respect to x, 2y $$dy\over … ## Find \(dy\over dx$$ where x = a{cos t + $${1\over 2} log tan^2 {t\over 2}$$} and y = a sin t

Solution : We have, x = a{cos t + $${1\over 2} log tan^2 {t\over 2}$$} and y = a sin t $$\implies$$ x = a{cos t + $${1\over 2} \times 2 log tan{t\over 2}$$} and y = a sin t $$\implies$$ x = a{cos t + {$$log tan{t\over 2}$$} and y = a sin t …

## What is the differentiation of cosx sinx ?

Solution : Let y = cosx.sinx By using product rule in differentiation, $$dy\over dx$$ = sinx(-sinx) + cosx.cosx $$dy\over dx$$ = $$cos^2x – sin^2x$$ = cos 2x Hence, the differentiation of cosx.sinx with respect to x is cos 2x. Questions for Practice What is the differentiation of $$e^{sinx}$$ ? What is the differentiation of sin …

## What is the differentiation of $$e^{sinx}$$ ?

Solution : Let y = $$e^{sinx}$$. Putting u = sinx , we get y = $$e^u$$ and u = sinx $$\therefore$$  $$dy\over du$$ = $$e^u$$ and $$du\over dx$$ = cosx Now, $$dy\over dx$$ = $$dy\over du$$ $$\times$$ $$du\over dx$$ $$\implies$$ $$dy\over dx$$ = $$e^u$$cosx = $$e^{sinx}$$cosx Hence, the differentiation of $$e^{sinx}$$ with respect to x …

## What is the differentiation of sin square x or $$sin^2x$$ ?

Solution : The differentiation of sin square x with respect to x is sin 2x. Explanation : We have, y = $$sin^2 x$$ Differentiating by using chain rule, $$dy\over dx$$ = 2 sin x cos x $$dy\over dx$$ = sin 2x Hence, $$dy\over dx$$ = sin 2x Questions for Practice What is the differentiation of …

## What is the differentiation of 1/sinx ?

Solution : We have, y = 1/sinx = cosecx By using differentiation formula of cosecx, $$dy\over dx$$ = -cosecx.cotx Hence, the differentiation of 1/sinx = -cosecx.cotx Questions for Practice What is the differentiation of $$e^{sinx}$$ ? What is the differentiation of sin square x or $$sin^2x$$ ? What is the differentiation of cosx sinx ? …

## What is the differentiation of $$sin x^2$$ ?

Solution : We have, y = $$sin x^2$$ Differentiating with respect to x by using chain rule, $$dy\over dx$$ = $$cos x^2$$.(2x) $$dy\over dx$$ = 2x.$$cos x^2$$ Hence, the differentiation of $$sin x^2$$ with respect to x is 2x.$$cos x^2$$ Questions for Practice What is the differentiation of $$e^{sinx}$$ ? What is the differentiation of …

## What is the differentiation of log sin x ?

Solution : We have, y = log sin x By using chain rule in differentiation, Let u = sin x $$\implies$$ $$du\over dx$$ = cos x And, y = log u $$\implies$$ $$dy\over du$$ = $$1\over u$$  Now, $$dy\over dx$$ = $$dy\over du$$ $$\times$$ $$du\over dx$$ $$\implies$$ $$dy\over dx$$ = $$1\over u$$ $$\times$$ cos x …

## What is the differentiation of 1/log x ?

Solution : We have, y = $$1\over log x$$ By using quotient rule in differentiation, $$dy\over dx$$ = $$log x.{d\over dx}(1) – 1 {d\over dx}(log x)\over (log x)^2$$ $$dy\over dx$$ = $$0 – {1\over x}\over (log x)^2$$ = $$-1\over x (log x)^2$$ Hence, the differentiation of 1/log x with respect to x is \(-1\over x …