Differentiate the following: y = sin2xcosx - Mathematics

Differentiate the following:

y = `(sin^2x)/cos x`

योग

y = `(sin^2x)/cos x`

`("d"y)/("d"x) = (cosx(2sinx cos x) - sin^2x xx - sin x)/(cos x)^2`

`("d"y)/("d"x) = (2sinx cos^2x + sin^3x)/(cos^2x)`

= `sin x ((2 cos^2 x + sin^2 x))/(cos^2x)`

= `sin x((2cos2x)/(cos^2x) + (sin2x)/(cos2x))`

= sin x(2 + tan²x)

= sin x(1 + 1 + tan²x)

`("d"y)/("d"x)` = sin x(1 + sec² x)

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अध्याय 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [पृष्ठ १६३]

अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 19 | पृष्ठ १६३

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 = e^x sin x

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 = e^-x . log x

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

Differentiate the following:

h(t) = `("t" - 1/"t")^(3/2)`

Differentiate the following:
y = e^–mx

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

Find the derivatives of the following:

(cos x)^{log x}

Find the derivatives of the following:
tan (x + y) + tan (x – y) = x