Advertisements
Advertisements
प्रश्न
Find `"dy"/"dx"`, if Differentiate 5x with respect to log x
Advertisements
उत्तर
Let u = 5x and v = log x
u = 5x
Differentiating both sides w.r.t.x, we get
`"du"/"dx" = 5^"x" * log 5`
v = log x
Differentiating both sides w.r.t.x, we get
`"dv"/"dx" = 1/"x"`
∴ `"du"/"dv" = (("du"/"dx"))/(("dv"/"dx")) = (5^"x" log 5)/(1/"x") = "x"*5^"x" (log 5)`
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"`, if x = e3t, y = `"e"^((4"t" + 5))`
Find `"dy"/"dx"`, if x = `("u" + 1/"u")^2, "y" = (2)^(("u" + 1/"u"))`
Solve the following.
If x = `"a"(1 - 1/"t"), "y" = "a"(1 + 1/"t")`, then show that `"dy"/"dx" = - 1`
If x = t . log t, y = tt, then show that `dy/dx - y = 0`.
If x = `y + 1/y`, then `dy/dx` = ____.
If x sin(a + y) + sin a cos(a + y) = 0 then show that `("d"y)/("d"x) = (sin^2("a" + y))/(sin"a")`
Choose the correct alternative:
If x = 2am, y = 2am2, where m be the parameter, then `("d"y)/("d"x)` = ?
If x = `"a"("t" - 1/"t")`, y = `"a"("t" + 1/"t")`, where t be the parameter, then `("d"y)/("d"x)` = ?
State whether the following statement is True or False:
If x = 2at, y = 2a, where t is parameter, then `("d"y)/("d"x) = 1/"t"`
State whether the following statement is True or False:
If x = 5m, y = m, where m is parameter, then `("d"y)/("d"x) = 1/5`
If x = `(4"t")/(1 + "t"^2)`, y = `3((1 - "t"^2)/(1 + "t"^2))`, then show that `("d"y)/("d"x) = (-9x)/(4y)`
If x = `sqrt(1 + u^2)`, y = `log(1 + u^2)`, then find `(dy)/(dx).`
Find `dy/dx` if, `x = e^(3t) , y = e^sqrtt`
Find `dy/dx` if, x = e3t, y = `e^((4t + 5))`
If x = f(t) and y = g(t) are differentiable functions of t, then prove that:
`dy/dx = ((dy//dt))/((dx//dt))`, if `dx/dt ≠ 0`
Hence, find `dy/dx` if x = a cot θ, y = b cosec θ.
Find the derivative of 7x w.r.t.x7
Find `dy/dx` if, x = `e^(3t)`, y = `e^(4t+5)`
Find `dy/dx if, x = e^(3t),y=e^((4t+5))`
Find `dy/dx` if,
`x = e ^(3^t), y = e^((4t + 5))`
Find `dy/dx if,x = e^(3^T), y = e^((4t + 5)`
Find `dy/dx` if x= `e^(3t)`, y =`e^((4t+5))`
Find `dy/dx` if, `x = e^(3t), y = e^((4t + 5))`
Find `dy/dx` if, x = `e^(3t)`, y = `e^((4t + 5))`.
