Find the derivatives of the following functions with respect to corresponding independent variables: g(t) = t3 cos t

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

g(t) = t³ cos t

बेरीज

g(t) = t³ cos t

(i.e.) u = t³ and v = cos t

Let u’ = `("d"u)/("d"x)` and v’ = `("d"v)/("d"x)` = (– sin t)

g'(t) = uv’ + vu’

g'(t) = t³ (– sin t) + cos t (3t²)

= – t³ sin t + 3t² cos t

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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 5 | पृष्ठ १६०

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

y = sin x + cos x

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 = `(tanx - 1)/secx`

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

y = cosec x . cot x

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

y = sin x⁰

Differentiate the following:
y = tan 3x

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

Differentiate the following:

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

Differentiate the following:
y = `sqrt(x +sqrt(x)`

Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`

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

Find the derivatives of the following:

(cos x)^{log x}