Find the derivatives of the following: x = atacos3t ; y = atasin3t

Find the derivatives of the following:

x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`

बेरीज

x = a cos^t , y = a sin³t

`("d"x)/("d"t) = 3"a"cos^2"t" (- sin"t")`, `("d"y)/("dt") = 3 "a"sin^2"t" (cos "t")`

`(("d"y)/("dt"))/(("d"x)/("dt")) = (3"a" sin^2"t" cos"t")/(- 3"a" cos^2"t" sin"t")`

`("d"y)/("d"x) = - (sin "t")/(cos "t")`

`("d"y)/("d"x)` = – tan t

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Differentiation Rules

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पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [पृष्ठ १७६]

पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 13 | पृष्ठ १७६

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

f(x) = x sin x

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 = `x/(sin x + cosx)`

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

y = `sinx/x^2`

Differentiate the following:
y = tan 3x

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

Differentiate the following:
F(x) = (x³ + 4x)⁷

Differentiate the following:

f(t) = `root(3)(1 + tan "t")`

Differentiate the following:

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

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

Find the derivatives of the following:

`tan^-1sqrt((1 - cos x)/(1 + cos x)`

Find the derivatives of the following:

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