Advertisements
Advertisements
Question
If y = log [cos(x5)] then find `("d"y)/("d"x)`
Advertisements
Solution
y = log [cos(x5)]
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x)[log{cos(x^5)}]`
= `1/(cos(x^5))*"d"/("d"x)[cos(x^5)]`
= `1/(cos(x^5))*[-sin(x^5)]*"d"/("d"x)(x^5)`
= `(-sin(x^5))/(cos(x^5))*5x^4`
= – 5x4 tan(x5)
RELATED QUESTIONS
Differentiate the function with respect to x.
(log x)cos x
Differentiate the function with respect to x.
(x + 3)2 . (x + 4)3 . (x + 5)4
Differentiate the function with respect to x.
`(x + 1/x)^x + x^((1+1/x))`
Differentiate the function with respect to x.
`(sin x)^x + sin^(-1) sqrtx`
Differentiate the function with respect to x.
`x^(xcosx) + (x^2 + 1)/(x^2 -1)`
Find `bb(dy/dx)` for the given function:
yx = xy
Find `bb(dy/dx)` for the given function:
xy = `e^((x - y))`
Find the derivative of the function given by f(x) = (1 + x) (1 + x2) (1 + x4) (1 + x8) and hence find f′(1).
if `x^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`
If `y = sin^-1 x + cos^-1 x , "find" dy/dx`
If ey ( x +1) = 1, then show that `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`
Find `(d^2y)/(dx^2)` , if y = log x
xy = ex-y, then show that `"dy"/"dx" = ("log x")/("1 + log x")^2`
Find `"dy"/"dx"` if y = xx + 5x
If y = (log x)x + xlog x, find `"dy"/"dx".`
If `log_5((x^4 + y^4)/(x^4 - y^4)) = 2, "show that""dy"/"dx" = (12x^3)/(13y^3)`.
If xy = ex–y, then show that `"dy"/"dx" = logx/(1 + logx)^2`.
`"If" y = sqrt(logx + sqrt(log x + sqrt(log x + ... ∞))), "then show that" dy/dx = (1)/(x(2y - 1).`
If ey = yx, then show that `"dy"/"dx" = (logy)^2/(log y - 1)`.
If x = `asqrt(secθ - tanθ), y = asqrt(secθ + tanθ), "then show that" "dy"/"dx" = -y/x`.
If x = a cos3t, y = a sin3t, show that `"dy"/"dx" = -(y/x)^(1/3)`.
If x = 2cos4(t + 3), y = 3sin4(t + 3), show that `"dy"/"dx" = -sqrt((3y)/(2x)`.
If x = sin–1(et), y = `sqrt(1 - e^(2t)), "show that" sin x + dy/dx` = 0
Differentiate 3x w.r.t. logx3.
Find the second order derivatives of the following : x3.logx
Find the second order derivatives of the following : log(logx)
If y = `log[sqrt((1 - cos((3x)/2))/(1 +cos((3x)/2)))]`, find `("d"y)/("d"x)`
If y = 5x. x5. xx. 55 , find `("d"y)/("d"x)`
Derivative of loge2 (logx) with respect to x is _______.
If y = `{f(x)}^{phi(x)}`, then `dy/dx` is ______
If y = tan-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.
`"d"/"dx" [(cos x)^(log x)]` = ______.
If `("f"(x))/(log (sec x)) "dx"` = log(log sec x) + c, then f(x) = ______.
`2^(cos^(2_x)`
If xm . yn = (x + y)m+n, prove that `"dy"/"dx" = y/x`
If y = `log ((1 - x^2)/(1 + x^2))`, then `"dy"/"dx"` is equal to ______.
If y `= "e"^(3"x" + 7), "then the value" |("dy")/("dx")|_("x" = 0)` is ____________.
If y = `x^(x^2)`, then `dy/dx` is equal to ______.
Derivative of log (sec θ + tan θ) with respect to sec θ at θ = `π/4` is ______.
If `log_10 ((x^2 - y^2)/(x^2 + y^2))` = 2, then `dy/dx` is equal to ______.
Find `dy/dx`, if y = (log x)x.
