Home
Class 11
PHYSICS
Find first derivative of y w.r.t. x. (...

Find first derivative of y w.r.t. x.
(i) `y=e^(-x)` , (ii) `y=4 sin 3x` , (iii) `y=4e^(x^(2)-2x)`

Text Solution

Verified by Experts

(i) `y=e^(-x)=e^(z)` where `z=-x " "` so `(dy)/(dx)=(dy)/(dz)xx(dz)/(dx)=(e^(z))(-1)=-e^(z)=-e^(-x)`
(ii) `y=4 sin 3x=4 sinz` where `z=3x " "` so `(dy)/(dx)=(dy)/(dz)xx(dz)/(dx)=4 (cos z)(3)=12 cos 3x`
(iii) `y=4e^(x^(2)-2x)=4e^(z)` where `z=x^(2)-2x " "` so `(dy)/(dx)=(dy)/(dz)xx(dz)/(dx)=4 (e^(z))(2x-2)=(8x-x)e^(x^(2)-2x)`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS

    ALLEN|Exercise Part -II Example|61 Videos

  • MISCELLANEOUS

    ALLEN|Exercise Part -II Example Some worked out Examples|1 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN|Exercise BEGINNER S BOX-7|8 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN|Exercise EXERCISE-IV|8 Videos

Similar Questions

Explore conceptually related problems

Find first derivation of y w.r.t. x. (i) y=x^(2) sin x , (ii) y=4(e^(x))cos x

Find differentiation of y w.r.t x. (i) y=(sin x)/x , (ii) y=(4x^(3))/e^(x)

The derivative of y=x^(2^(x)) w.r.t. x is

The derivative of y = x^2logx w.r.t. x is :

Find the derivative of y=sin(x^2-4) .

Find differentiation of y w.r.t x. (i) y=x^(2)-6x (ii) y=x^(5)+2e^(x) (iii) y=4 ln x +cos x

Find the derivative of the following w.r.t. x : x-y=pi

find the derivative of e^(x) + e^(y) = e^(x +y)

Find derivative of (e^(x))/(sin x) w.r.t.to x

find the derivative of y=e^(sin sqrt(x))