If f(x) = ex, h(x) = (fof) (x), then \(\frac{h'(x)}{h'(x)}\) =
If f(x) = ex, h(x) = (fof) (x), then \(\frac{h'(x)}{h'(x)}\) =
h(x)
\(\frac{1}{h(x)}\)
\(log h(x)\)
\(-log h(x)\)
The Correct Option is C
Solution and Explanation
The correct option is: (C) \(log h(x)\)
Top Questions on Tangents and Normals
The portion of the line \( 4x + 5y = 20 \) in the first quadrant is trisected by the lines \( L_1 \) and \( L_2 \) passing through the origin. The tangent of an angle between the lines \( L_1 \) and \( L_2 \) is:
- JEE Main - 2024
- Mathematics
- Tangents and Normals
- If A is the area in the first quadrant enclosed by the curve \(C: 2x^2 – y + 1 = 0\), the tangent to C at the point (1, 3) and the line x + y = 1, then the value of 60A is ________
- JEE Main - 2023
- Mathematics
- Tangents and Normals
- Let a curve y = f(x), x ∈ (0, ∞) pass through the points \(p ( 1\frac{3 }{2} )\) and Q \( ( a,\frac{1 }{2} )\). If the tangent at any point R(b, f(b)) to the given curve cuts the y-axis at the point S (0, c) such that bc = 3, then (PQ)2 is equal to ______.
- JEE Main - 2023
- Mathematics
- Tangents and Normals
- The tangents at the point $A (1,3)$ and $B (1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$ Then the area (in unit $^2$ ) of $\triangle PAB$ is :-
- JEE Main - 2023
- Mathematics
- Tangents and Normals
The number of points on the curve \(y=54 x^5-135 x^4-70 x^3+180 x^2+210 x\) at which the normal lines are parallel \(to x+90 y+2=0\) is
- JEE Main - 2023
- Mathematics
- Tangents and Normals
Questions Asked in TS EAMCET exam
If A is a square matrix of order 3, then |Adj(Adj A2)| =
- TS EAMCET - 2023
- Algebra of Complex Numbers
Match the following List -I (Complex) List II (Spin only Magnetic Moment)
List -I (Complex) List II (Spin only Magnetic Moment) A) [CoF6]3- I) 0 B) [Co(C2O4)3]3- II) √24 C) [FeF6]3+ III) √8 D) [Mn(CN)6]3- IV) √35 V) √15 the correct answer is:
- TS EAMCET - 2023
- coordination compounds
If (h,k) is the image of the point (3,4) with respect to the line 2x - 3y -5 = 0 and (l,m) is the foot of the perpendicular from (h,k) on the line 3x + 2y + 12 = 0, then lh + mk + 1 = 2x - 3y - 5 = 0.
- TS EAMCET - 2023
- Coordinate Geometry
If a line ax + 2y = k forms a triangle of area 3 sq.units with the coordinate axis and is perpendicular to the line 2x - 3y + 7 = 0, then the product of all the possible values of k is
- TS EAMCET - 2023
- Algebra of Complex Numbers
- If the solution of the differential equation \(\frac{dy}{dx}=\frac{2x+3y}{3x-2y}\) is y = xtan(f(x)) + c then f(x) =
- TS EAMCET - 2023
- Differential equations
Concepts Used:
Tangents and Normals
- A tangent at a degree on the curve could be a straight line that touches the curve at that time and whose slope is up to the derivative of the curve at that point. From the definition, you'll be able to deduce the way to realize the equation of the tangent to the curve at any point.
- Given a function y = f(x), the equation of the tangent for this curve at x = x0
- Slope of tangent (at x=x0) m=dy/dx||x=x0
- A normal at a degree on the curve is a line that intersects the curve at that time and is perpendicular to the tangent at that point. If its slope is given by n, and also the slope of the tangent at that point or the value of the derivative at that point is given by m. then we got
m×n = -1
- The normal to a given curve y = f(x) at a point x = x0
- The slope ‘n’ of the normal: As the normal is perpendicular to the tangent, we have: n=-1/m
Diagram Explaining Tangents and Normal:
SUBSCRIBE TO OUR NEWS LETTER
