Advertisements
Advertisements
Question
If y = log [cos(x5)] then find `("d"y)/("d"x)`
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 following function with respect to x: `(log x)^x+x^(logx)`
Differentiate the function with respect to x.
`x^x - 2^(sin x)`
Differentiate the function with respect to x.
`(sin x)^x + sin^(-1) sqrtx`
Differentiate the function with respect to x.
xsin x + (sin x)cos x
Find `dy/dx`for the function given in the question:
xy + yx = 1
Find `dy/dx` for the function given in the question:
(cos x)y = (cos y)x
Find `dy/dx` for the function given in the question:
`xy = e^((x – y))`
If cos y = x cos (a + y), with cos a ≠ ± 1, prove that `dy/dx = cos^2(a+y)/(sin a)`
if `x^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`
Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`
Evaluate
`int 1/(16 - 9x^2) dx`
Find `"dy"/"dx"` , if `"y" = "x"^("e"^"x")`
Differentiate : log (1 + x2) w.r.t. cot-1 x.
Find `"dy"/"dx"` if y = xx + 5x
If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`
If log (x + y) = log(xy) + p, where p is a constant, then prove that `"dy"/"dx" = (-y^2)/(x^2)`.
If `log_10((x^3 - y^3)/(x^3 + y^3)) = 2, "show that" "dy"/"dx" = -(99x^2)/(101y^2)`
If y = `x^(x^(x^(.^(.^.∞))`, then show that `"dy"/"dx" = y^2/(x(1 - logy).`.
If x = `asqrt(secθ - tanθ), y = asqrt(secθ + tanθ), "then show that" "dy"/"dx" = -y/x`.
If x = log(1 + t2), y = t – tan–1t,show that `"dy"/"dx" = sqrt(e^x - 1)/(2)`.
If y = log (log 2x), show that xy2 + y1 (1 + xy1) = 0.
Choose the correct option from the given alternatives :
If xy = yx, then `"dy"/"dx"` = ..........
If f(x) = logx (log x) then f'(e) is ______
If y = `25^(log_5sin_x) + 16^(log_4cos_x)` then `("d"y)/("d"x)` = ______.
If y = `log[4^(2x)((x^2 + 5)/sqrt(2x^3 - 4))^(3/2)]`, find `("d"y)/("d"x)`
If y = 5x. x5. xx. 55 , find `("d"y)/("d"x)`
If x7 . y5 = (x + y)12, show that `("d"y)/("d"x) = y/x`
The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290 K and the metal temperature drops from 370 K to 330 K in 1 O min, then the time required to drop the temperature upto 295 K.
lf y = `2^(x^(2^(x^(...∞))))`, then x(1 - y logx logy)`dy/dx` = ______
Derivative of `log_6`x with respect 6x to is ______
`2^(cos^(2_x)`
`log (x + sqrt(x^2 + "a"))`
`lim_("x" -> 0)(1 - "cos x")/"x"^2` is equal to ____________.
`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)` is equal to ____________.
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 ______.
If y = `log(x + sqrt(x^2 + 4))`, show that `dy/dx = 1/sqrt(x^2 + 4)`
If y = `9^(log_3x)`, find `dy/dx`.
Evaluate:
`int log x dx`
Find the derivative of `y = log x + 1/x` with respect to x.
