Advertisements
Advertisements
Question
Differentiate the following w.r.t. x:
`e^x/sinx`
Advertisements
Solution
Let, y = `e^x/sin x`
Differentiating both sides with respect to x,
`dy/dx = d/dx(e^x/sin x)`
= `(sin x d/dx e^x - e^x d/dx sin x)/(sin^2 x)`
= `(sin x . e^x - e^x . cos x)/(sin^2 x)`
= `(e^x (sin x - cos x))/(sin^2x)`, x ≠ xπ, n ∈ Z
APPEARS IN
RELATED QUESTIONS
Differentiate the following w.r.t. x:
sin (tan–1 e–x)
Differentiate the following w.r.t. x:
`sqrt(e^(sqrtx))`, x > 0
Differentiate the function with respect to x:
(log x)log x, x > 1
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 = ex–y, prove that `("d"y)/("d"x) = logx/(1 + logx)^2`
The derivative of log10x w.r.t. x is ______.
If x = `e^(x/y)`, then prove that `dy/dx = (x - y)/(xlogx)`.
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" = (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 `"xy"^2 = "ax"^2 + "bxy" + "y"^2, "then find" "dy"/"dx"`
If f(x) = `"log"_("x"^2) ("log x")`, then f(e) 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 \[\frac{d}{dx}(e^x)\]?
Which expression gives the change of base rule?
Which expression gives the power rule for logarithms?
Which inverse property is valid only for \[x>0\]?
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?
The graph of \[y=\log_b x\] is a mirror image of which graph reflected perfectly across \[y=x\]?
Which pair of graphs are reflections of each other about \[y=x\]?
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 \[x\].
Which list contains the main log laws?
