Differentiate the following: y = exe-x2

Differentiate the following:

y = `x"e"^(-x^2)`

Sum

y = `x"e"^(-x^2)`

y = uv where u = x and v = `"e"^(-x^2)`

Now u’ = 1 and v’ = `"e"^(-x^2) (- 2x)`

v’ = `- 2x"e"^(-x^2)`

Now y = uv

⇒ y’ = uv’ + vu’

(i..e.) `("d"y)/("d"x) = x[- 2x"e"^(-x^2)] + "e"^(-x^2) (1)`

= `"e"^(- x^2) (1 - 2x^2)`

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [Page 163]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 15 | Page 163

Find the derivatives of the following functions with respect to corresponding independent variables:

y = `tan x/x`

Find the derivatives of the following functions with respect to corresponding independent variables:

y = e^-x . log x

Find the derivatives of the following functions with respect to corresponding independent variables:

y = log₁₀ x

Differentiate the following:
y = `"e"^sqrt(x)`

Differentiate the following:
y = sin (e^x)

Differentiate the following:

s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`

Differentiate the following:
y = sin³x + cos³x

Differentiate the following:
y = `sin(tan(sqrt(sinx)))`

Find the derivatives of the following:

(cos x)^{log x}

Find the derivatives of the following:

`tan^-1 = ((6x)/(1 - 9x^2))`

Find the derivatives of the following:

x = a (cos t + t sin t); y = a (sin t – t cos t)

Find the derivatives of the following:

x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`

Find the derivatives of the following:

sin^-1 (3x – 4x³)

Find the derivatives of the following:

If y = sin^–1x then find y”