Advertisements
Advertisements
प्रश्न
The derivative of x2x w.r.t. x is ______.
पर्याय
x2x – 1
2x2x log x
2x2x (1 + log x)
2x2x (1 – log x)
Advertisements
उत्तर
The derivative of x2x w.r.t. x is 2x2x (1 + log x).
Explanation:
Let y = x2x
log y = 2x log x ...(Taking log on both sides)
Differentiating w.r.t. x,
`1/y dy/dx` = 2[1 + log x]
`\implies dy/dx` = 2x2x [1 + log x]
संबंधित प्रश्न
If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`
Differentiate the function with respect to x.
xx − 2sin x
Differentiate the function with respect to x.
(log x)x + xlog x
Differentiate the function with respect to x.
`(sin x)^x + sin^(-1) sqrtx`
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 = a (cos t + t sin t) and y = a (sin t – t cos t), find `(d^2y)/dx^2`.
Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`
Differentiate
log (1 + x2) w.r.t. tan-1 (x)
If y = (log x)x + xlog x, find `"dy"/"dx".`
If log (x + y) = log(xy) + p, where p is a constant, then prove that `"dy"/"dx" = (-y^2)/(x^2)`.
If xy = ex–y, then show that `"dy"/"dx" = logx/(1 + logx)^2`.
If x = log(1 + t2), y = t – tan–1t,show that `"dy"/"dx" = sqrt(e^x - 1)/(2)`.
If x = sin–1(et), y = `sqrt(1 - e^(2t)), "show that" sin x + dy/dx` = 0
Choose the correct option from the given alternatives :
If xy = yx, then `"dy"/"dx"` = ..........
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.
If y = tan-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.
If y = `("e"^"2x" sin x)/(x cos x), "then" "dy"/"dx" = ?`
`8^x/x^8`
If y = `(1 + 1/x)^x` then `(2sqrt(y_2(2) + 1/8))/((log 3/2 - 1/3))` 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 the derivative of `y = log x + 1/x` with respect to x.
If xy = yx, then find `dy/dx`
What is logarithmic differentiation?
What is the first step in the standard procedure for \[y=[u(x)]^{v(x)}\]?
After differentiating \[\log y=v(x)\cdot\log[u(x)]\], which equation is obtained?
What is \[\frac{1}{y}\cdot\frac{dy}{dx}\] for \[y=\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\]?
What condition must be ensured for an expression inside logarithm?
