Advertisements
Advertisements
Question
Differentiate the following w.r.t. x:
log (cos ex)
Advertisements
Solution
Let, y = log (cos ex)
Differentiating both sides with respect to x,
`dy/dx= d/dx log (cos e^x)`
= `1/(cos e^x) d/dx (cos e^x)`
= `1/(cos e^x) (- sin e^x) d/dx e^x`
= `-(sin e^x)/(cos e^x) * e^x`
= −ex tan ex
APPEARS IN
RELATED QUESTIONS
Differentiate the following w.r.t. x:
sin (tan–1 e–x)
Differentiate the following w.r.t. x:
log (log x), x > 1
Differentiate the following w.r.t. x:
cos (log x + ex), x > 0
Differentiate the function with respect to x:
cos (a cos x + b sin x), for some constant a and b.
If `"y" ="x"^"x" , "find" "dy"/"dx"`.
If xy - yx = ab, find `(dy)/(dx)`.
If `"x" = "e"^(cos2"t") "and" "y" = "e"^(sin2"t")`, prove that `(d"y")/(d"x") = - ("y"log"x")/("x"log"y")`.
If xy = ex–y, prove that `("d"y)/("d"x) = logx/(1 + logx)^2`
The derivative of log10x w.r.t. x is ______.
Find `"dy"/"dx"`, if y = `x^tanx + sqrt((x^2 + 1)/2)`
If `"y = a"^"x", "b"^(2"x" -1), "then" ("d"^2"y")/"dx"^2` is ____________.
If `"y"^2 = "ax"^2 + "bx + c", "then" "d"/"dx" ("y"^3 "y"_"z") =` ____________.
If `sqrt(("x + y")) + sqrt (("y - x")) = "a", "then" "dy"/"dx" =` ____________.
If `"y = tan"^-1 [("sin x + cos x")/("cos x - sin x")], "then" "dy"/"dx"` is equal to ____________.
The domain of the function defined by f(x) = logx 10 is
Which function is an exponential function?
For positive values of \[x\], which expression grows faster than \[x^n\] for any fixed positive integer \[n\] when \[x\] is sufficiently large?
What is \[\frac{d}{dx}(e^x)\]?
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 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?
What is the range of the logarithmic function \[y=\log_b x\]?
The graph of \[y=\log_b x\] is a mirror image of which graph reflected perfectly across \[y=x\]?
If \[y=b^x\], which equivalent logarithmic statement is correct?
Which pair of graphs are reflections of each other about \[y=x\]?
Differentiate \[e^{-x}\] with respect to \[x\].
Differentiate \[\cos^{-1}(e^x)\] with respect to \[x\].
