Write the degree of the differential equation : $x\left(\frac{d^{2}y}{d x^{2}}\right)^{3}+y\left(\frac{d y}{d x}\right)^{4}+x^{3}=0$

Write the degree of the differential equation : $\left(\frac{d y}{d x}\right)^{4}+3x\frac{d^{2}y}{d x^{2}}=0.$

Write the order of the differential equation: $\log\,\left(\frac{d^{2}y}{d x^{2}}\right)=\left(\frac{d y}{d x}\right)^{3}+x$

Write the sum of the order and degree of the differential equation $1+\left(\frac{d y}{d x}\right)^{4}=7\left(\frac{d^{2}y}{d x^{2}}\right)^{3}\,.$

Using derivative, find the approximate percentage increase in the area of a circle if its radius is increased by 2%.

If f : R → R and g : R → R are given by f(x) = sin x and g(x) = 5x² then find gof(x)

If f : R → R is defined by f(x) = $(3-x^{3})^{1/3},$ then find fof(x).

If f : R → R is defined by f(x) = 3x + 2, then define f [f(x)].

If f(x) = 27x³ and g(x) = $x^{1/3}$, then find gof(x).

Write fog, if f : R → R and g : R → R are given by f(x) = 8x³ and g(x) = $x^{1/3}.$

Write fog, if f : R → R and g : R → R are given by f(x) = |x| and g(x) = |5x - 2|.

Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} given by f = {(1, 2) (3, 5) (4, 1)} and g = {(1, 3), (2, 3), (5, 1)} Write down gof.

The contentment obtained after eating x-units of a new dish at a trial function is given by the function $f(x)=x^{3}+6x^{2}+5x+3.$. If the marginal contentment is defined as the rate of change of f(x) with respect to the number of units consumed at an instant, then find the marginal contentment when three units of dish are consumed.

Find the magnitude of each of the vectors $\stackrel{\rightarrow}{a}$ and $\stackrel{\rightarrow}{b}$,having the same magnitude such that the angle between them is 60° and their scalar product is ${\frac{9}{2}}.$

Let f : R → R be defined by f(x) = 3x² – 5 and g : R → R be defined by g(x) =${\frac{x}{x^{2}+1}}.$ find gof(x) .