Advertisements
Advertisements
Question
Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`
Solution
y = `"a"^((1 + log "x"))`
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = "d"/"dx" "a"^((1 + log "x"))`
`= "a"^((1 + log "x")) * log "a" * "d"/"dx" (1 + log "x")`
`= "a"^((1 + log "x")) * log "a" * (0 + 1/"x")`
∴ `"dy"/"dx" = "a"^((1 + log "x")) * log "a" * 1/"x"`
APPEARS IN
RELATED QUESTIONS
If y = eax. cos bx, then prove that
`(d^2y)/(dx^2) - 2ady/dx + (a^2 + b^2)y` = 0
Find `dy/dx if x^2y^2 - tan^-1(sqrt(x^2 + y^2)) = cot^-1(sqrt(x^2 + y^2))`
Find `"dy"/"dx"` if xey + yex = 1
Find `"dy"/"dx"` if, y = `sqrt("x" + 1/"x")`
Find `"dy"/"dx"` if, y = log(ax2 + bx + c)
Fill in the Blank
If 3x2y + 3xy2 = 0, then `"dy"/"dx"` = ________
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25 + 30x – x2.
Suppose y = f(x) is a differentiable function of x on an interval I and y is one – one, onto and `("d"y)/("d"x)` ≠ 0 on I. Also if f–1(y) is differentiable on f(I), then `("d"x)/("d"y) = 1/(("d"y)/("d"x)), ("d"y)/("d"x)` ≠ 0
If y = x10, then `("d"y)/("d"x)` is ______
Derivative of ex sin x w.r.t. e-x cos x is ______.
If y = (sin x2)2, then `("d"y)/("d"x)` is equal to ______.
Differentiate `sqrt(tansqrt(x))` w.r.t. x
If y = `sin^-1 {xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)}` and 0 < x < 1, then find `("d"y)/(dx)`
If x = a sec3θ and y = a tan3θ, find `("d"y)/("d"x)` at θ = `pi/3`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`
Solve the following:
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10`x + 25x^2`
