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

बेरीज

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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Differentiation Rules

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पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.2 [पृष्ठ १६०]

पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.2 | Q 7 | पृष्ठ १६०

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

g(t) = 4 sec t + tan t

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)`

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

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

Differentiate the following:

f(x) = `x/sqrt(7 - 3x)`

Differentiate the following:

y = `5^((-1)/x)`

Differentiate the following:
y = (1 + cos²)⁶

Find the derivatives of the following:
y = `x^(logx) + (logx)^x`

Find the derivatives of the following:

`sqrt(x^2 + y^2) = tan^-1 (y/x)`

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

Find the derivatives of the following:

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

Find the derivatives of the following:

`cos^-1 ((1 - x^2)/(1 + x^2))`

Find the derivatives of the following:

If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x²)y₂ – 3xy₁ – y = 0

Find the derivatives of the following:

If sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ