Questions from General Calculus

Q: Differentiate. J(v) = (v3 - 2v

Differentiate. J(v) = (v3 - 2v)(v-4 + v-2)

Q: Find dy/dx by implicit differentiation. 2x2 + xy

Find dy/dx by implicit differentiation. 2x2 + xy - y2 = 2

Q: Differentiate. f (z) = (1 – ez

Differentiate. f (z) = (1 – ez)(z + ez)

Q: Differentiate. y = x2 + 1 / x3 + 1

Differentiate. y = x2 + 1 / x3 + 1

Q: Differentiate the function. B(y) = cy-

Differentiate the function. B(y) = cy-6

Q: Differentiate. y = 1 t 3

Differentiate. y = 1 t 3 + 2 t 2 – 1

Q: (a) If f (x) = (x2 –

(a) If f (x) = (x2 – 1) / (x2 + 1), find f ‘(x) and f ‘’(x). (b) Check to see that your answers to part (a) are reasonable by comparing the graphs of f , f ‘, and f ‘’.

Q: (a) If f (x) = (x2 –

(a) If f (x) = (x2 – 1) ex, find f ‘(x) and f ‘’(x). (b) Check to see that your answers to part (a) are reasonable by comparing the graphs of f , f ‘, and f ‘’.

Q: Use logarithmic differentiation to find the derivative of the function.

Use logarithmic differentiation to find the derivative of the function. y = xx

Q: If f (x) = x2 / (1 + x

If f (x) = x2 / (1 + x), find f “(1).