Differentiate the following: y = 5-1x

Differentiate the following:

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

Sum

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

y = `"e"log^(5 - 1/x)`

y = `"e"^(- 1/xlog 5)`

`("d"y)/("d"x) = "e"^(- 1/x log 5) xx "d"/("d"x) (- 1/x log 5)`

= `"e"^(- 1/x log 5) xx - log 5((-1) x^(- 1 - 1))`

= `"e"^(- 1/x log 5) xx (log 5) x^(- 2)`

= `"e"^(log 5 - 1/x) ((log 5))/x^2`

`("d"y)/("d"x) = (5^(-1/x) (log 5))/x^2`

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [Page 163]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 20 | Page 163

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 = tan θ (sin θ + cos θ)

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

y = sin x⁰

Differentiate the following:
y = (x² + 4x + 6)⁵

Differentiate the following:
y = tan 3x

Differentiate the following:
y = cos (a³ + x³)

Differentiate the following:

y = `(x^2 + 1) root(3)(x^2 + 2)`

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:
`sqrt(x) = "e"^((x - y))`

Find the derivatives of the following:

(cos x)^{log x}