हिंदी

Differentiate the following w.r.t. x: log (log x), x > 1

Advertisements
Advertisements

प्रश्न

Differentiate the following w.r.t. x:

log (log x), x > 1

योग
Advertisements

उत्तर

Let, y = log (log x)

Differentiating both sides with respect to x,

`dy/dx = d/dx log (log x)`

= `1/(log x) d/dx log x`

= `1/(log x) * 1/x`

= `1/(x log x)`, x > 1

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Continuity and Differentiability - Exercise 5.4 [पृष्ठ १७४]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 5 Continuity and Differentiability
Exercise 5.4 | Q 8 | पृष्ठ १७४

संबंधित प्रश्न

Differentiate 3x w.r.t. log3x


Differentiate the following w.r.t. x:

`e^x/sinx`


Differentiate the following w.r.t. x:

`e^(x^3)`


Differentiate the following w.r.t. x: 

sin (tan–1 e–x)


Differentiate the following w.r.t. x: 

`cos x/log x`, x > 0


Differentiate the following w.r.t. x:

cos (log x + ex), x > 0


Differentiate the function with respect to x:

(log x)log x, x > 1


Differentiate the function with respect to x:

cos (a cos x + b sin x), for some constant a and b.


Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.


 If `"y" ="x"^"x" , "find"  "dy"/"dx"`.


If xy - yx = ab, find `(dy)/(dx)`.


The derivative of log10x w.r.t. x is ______.


If yx = ey – x, prove that `"dy"/"dx" = (1 + log y)^2/logy`


Find `"dy"/"dx"`, if y = `x^tanx + sqrt((x^2 + 1)/2)`


If `"y" = (varphi "n x")/"x",` then the value of y'' (e) is ____________.


If `"y"^2 = "ax"^2 + "bx + c", "then"  "d"/"dx" ("y"^3 "y"_"z") =` ____________.


If `"y = tan"^-1 [("sin x + cos x")/("cos x - sin x")], "then"  "dy"/"dx"` is equal to ____________.


What is \[\frac{d}{dx}(\log x)\] for \[x>0\]?


Which expression gives the change of base rule?


Which expression gives the product rule for logarithms?


Which expression gives the quotient rule for logarithms?


Which inverse property is valid only for \[x>0\]?


What is the domain of the exponential function \[y=b^x\]?


What is the range of the exponential function \[y=b^x\]?


Through which point does every graph of \[y=b^x\] pass?


Through which point does every graph of \[y=\log_b x\] pass?


For \[x>0\], differentiate \[\sin(\log x)\] with respect to \[x\].


Differentiate \[\cos^{-1}(e^x)\] with respect to \[x\].


Differentiate \[e^{\cos x}\] with respect to \[x\].


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×