Q1 of 147 Page 181

If x and y are connected parametrically by the equations given in without eliminating the parameter, Find dy/dx.
x = 2at², y = at⁴

It is given that

x = 2at², y = at⁴

So, now

= 2a.2t

= 4at ………… (1)

And

= a.4.t³

= 4at³………… (2)

Therefore, form equation (1) and (2). we get

Hence, the value of is t²

Differentiate (x² – 5x + 8) (x³ + 7x + 9) in three ways mentioned below:

(i) by using product rule

(ii) by expanding the product to obtain a single polynomial.

(iii) by logarithmic differentiation.

Do they all give the same answer?

If u, v and w are functions of x, then show that

in two ways – first by repeated application of product rule, second by logarithmic differentiation.

If x and y are connected parametrically by the equations given in without eliminating the parameter, Find dy/dx.

x = a cos θ, y = b cos θ

If x and y are connected parametrically by the equations given in without eliminating the parameter, Find dy/dx.

x = sin t, y = cos 2t

If x and y are connected parametrically by the equations given in without eliminating the parameter, Find dy/dx.x = 2at2, y = at4