Questions from General Calculus

Q: Prove the formulas given in Table 6 for the derivatives of the

Prove the formulas given in Table 6 for the derivatives of the following functions. (a) cosh-1 (b) tanh-1 (c) csch-1 (d) sech-1 (e) coth-1 Table 6:

Q: Find the derivative. Simplify where possible. f(x

Find the derivative. Simplify where possible. f(x) = ex cosh x

Q: Find the derivative. Simplify where possible. g(x

Find the derivative. Simplify where possible. g(x) = sinh2 x

Q: Find the derivative. Simplify where possible. h(x

Find the derivative. Simplify where possible. h(x)= sinh (x2)

Q: Find the derivative. Simplify where possible. F(t

Find the derivative. Simplify where possible. F(t) = ln (sinh t)

Q: Find the derivative. Simplify where possible. G(t

Find the derivative. Simplify where possible. G(t) = sinh (ln t)

Q: Use implicit differentiation to find an equation of the tangent line to

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4, ( -3√3 , 1) (astroid)

Q: Find the derivative. Simplify where possible. y = sech

Find the derivative. Simplify where possible. y = sech x (1 + ln sech x)

Q: A particle moves on a vertical line so that its coordinate at

A particle moves on a vertical line so that its coordinate at time t is y = t3 - 12t + 3, t ≥ 0. (a) Find the velocity and acceleration functions. (b) When is the particle moving upward and when is it...

Q: How many lines are tangent to both of the circles x2 +

How many lines are tangent to both of the circles x2 + y2 = 4 and x2 + (y – 3)2 = 1? At what points do these tangent lines touch the circles?