Find the derivatives of the following functions with respect to corresponding independent variables: y = ex sin x

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

y = e^x sin x

Sum

y = e^x sin x

⇒ y = uv’ + vu’

Now u = e^x

⇒ u’ = `("d"u)/("d"x) "e"^x`

v = sin x

⇒ v’ = `("d"v)/("d"x)` cos x

i.e. y’ = e^x (cos x) + sin x (e^x)

= e^x [sin x + cos x]

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.2 [Page 160]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.2 | Q 7 | Page 160

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 = `sinx/(1 + cosx)`

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

y = `sinx/x^2`

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

Draw the function f'(x) if f(x) = 2x² – 5x + 3

Differentiate the following:
y = `root(3)(1 + x^3)`

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

Differentiate the following:
y = (2x – 5)⁴ (8x² – 5)^–3

Differentiate the following:

y = `"e"^(3x)/(1 + "e"^x`

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

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

Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`