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
- Two lines \(L_1 \;\& \;L_2\) passing through origin trisecting the line segment intercepted by the line \(4x + 5y = 20\) between the coordinate axes. Then the tangent of angle between the lines \(L_1\) and \(L_2\) is
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- 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 ________
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- 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 ______.
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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
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Questions Asked in TS EAMCET exam
If cosθ = \(\frac{-3}{5}\)- and π < θ < \(\frac{3π}{2}\), then tan \(\frac{ θ}{2}\) + sin \(\frac{ θ}{2}\)+ 2cos \(\frac{ θ}{2}\) =
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Three long, straight, parallel wires carrying different currents are arranged as shown in the diagram. In the given arrangement, let the net force per unit length on the wire C be F. If the wire B is removed without disturbing the other two wires, then the force per unit length on wire A is:
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The alkali metal with the lowest E M- M+ (V) is X and the alkali metal with highest E M- M+ is Y. Then X and Y are respectively:
The number of significant figures in the measurement of a length 0.079000 m is:
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The roots of the equation x4 + x3 - 4x2 + x + 1 = 0 are diminished by h so that the transformed equation does not contain x2 term. If the values of such h are α and β, then 12(α - β)2 =
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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:
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