Differential Calculus-I

nth derivatives problems Find the nth derivative of 3^2x Find the nth derivative of x/(x+2) Find the nth derivative of y=e^2x cosh 4x Find the nth derivative of log(1+6x+9x^2) Find the nth derivative of log(sqrt(4x^2+8x+3)) Find the nth derivative of sin^2x Find the nth derivative of sin4x cos2x Find the nth derivative of e^2x cos3x Find the nth derivative of cos^4x Find the nth derivative of x/((x+1)(x-2)) Find the nth derivative of 6x/((x^2-4)(x-1)) Find the nth derivative of x^4/((x-1)(x-2)) Find…

Radius of curvature Centre of curvature Circle of curvature Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of curvature of the curve r^n=a^n sin(n theta) Find the radius of curvature for the curve r=a (1+cos(theta)) Find the radius of curvature of…

Leibnitz’s theorem Leibnitz's theorem, also known as the product rule for differentiation of two functions, is a formula that allows us to find the nth derivative of a product of two functions. Leibnitz's theorem is a powerful tool for calculating higher order derivatives. It can be extended to find the nth derivative of a product of more than two functions, by applying the formula recursively. Leibnitz's theorem has many applications in mathematics and physics, including the study of partial differential…

Pedal equation of a polar curve Pedal equation of a polar curve is expressed in terms of ‘p’ and ‘r’. It is also called as the p-r equation of the polar curve. Let r=f(θ) be the equation of a polar curve. To obtain the pedal equation of the polar curve r=f(θ), we have to eliminate ‘φ’ and ‘θ’ from the equations Steps to follow to find the pedal equation of the polar curve Topic Pedal equation of a polar curve…

Angle between two polar curves Steps to find the angle between two curves Topic Angle between two polar curves Problems Find the angle between the pair of curves r=6cos(theta) & r=2(1+cos(theta)) Find angle between the curves r=a/ (1+cos(theta)) and r=b/ (1-cos(theta)) Find the angle of intersection of the curves r=a(1+sin(theta)) and r=a(1-sin(theta)) Find the angle between the curves r^2 sin(2theta)=4 and r^2=16 sin(2theta) Find the angle between the polar curves r=a(1-cos(theta)) and r=b(1+cos(theta)) Show that the curves r^n=a^n cos(n theta)…