English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Find the derivatives of the following functions with respect to corresponding independent variables: y = log10 x - Mathematics

Advertisements
Advertisements

Question

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

y = log10 x

Sum

Solution

y = log10 x

y = logex . log10

`("d"y)/("d"x) = log_10"e"[1/x]`

= `(log_10"e")/x`

shaalaa.com
Differentiation Rules
  Is there an error in this question or solution?
Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.2 [Page 160]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.2 | Q 19 | Page 160

RELATED QUESTIONS

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

f(x) = x – 3 sin x


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:

y = cosec x . cot x


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

y = sin x


Differentiate the following:
y = cos (tan x)


Differentiate the following:

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


Differentiate the following:
y = e–mx 


Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3 


Find the derivatives of the following:

`x^2/"a"^2 + y^2/"b"^2` = 1


Find the derivatives of the following:

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


Find the derivatives of the following:

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


Find the derivatives of the following:

x = a (cos t + t sin t); y = a (sin t – t cos t)


Find the derivatives of the following:

Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`


Find the derivatives of the following:

If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`


Find the derivatives of the following:

If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y2 when x = 0


Choose the correct alternative:

If y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` is 


Choose the correct alternative:

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


Choose the correct alternative:

If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is


Choose the correct alternative:

The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×