If w=e^xy,x=at²,y=2at, find \(\frac { dw }{ dt } \)

If w=log(x²+y²),x=cosθ,y=sinθ, find \(\frac { dw }{ d\theta } \)

If \(w={ e }^{ { x }^{ 2 }+{ y }^{ 2 } }\) ,x=cosθ,y=sinθ, find \(\frac { dw }{ d\theta } \)

If w=xye^xy find \(\frac { { \partial }^{ 2 }u }{ \partial x\partial y } \)

Using differentials, find the approximate value of \(sin\left( \frac { 22 }{ 14 } \right) \) 

The pressure P and the volume V of a gas are connected by the relation PV^1.4=constant. Find the % error in P corresponding to a devreased of \(\frac { 1 }{ 2 } \%\) in V.

Find a linear approximation to f(x)=3xe^2x-10 at x=5

Without using any kind of computational aid use linear approximation to find the value of e^0.1

If y = x³ + 2x² find dy when x = 2 and dx =0.1

Compute the values of, \(\Delta\)y and dv if y = x³ + x² - 2x + 1 where x changes from 2 to 2.45

The radius of a sphere was measured and found to be 21 cm with a possible error in measurement of atmost 0.05 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere?

A circular template has a radius of 10 cm (\(\pm\) 0.02). Determine the possible error in calculating the area of the templates.

Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%.

Find the differential of the function
(i) \(y=\sqrt{x^{4}+x^{2}+1}\)
(ii) \(y=\frac{x-2}{2 x+3}\)

Find the differential dy and evaluate dy for the given values of x and dx.
(i) y = (x²+ 5)³, x = 1, dx = 0.05
(ii) y = cos x, x = \(\pi / 6\), dx = 0.05