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{y}={e}^{{{{{x}}}^{{{3}}}}}

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$y = e^{s i n x^{3}}$

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Practice questions from similar books

Question 1

Differentiate

tan^{- 1} (\frac{1 + x ^{2} - 1}{x})

with respect to

tan^{- 1} x,

when

x \neq = 0 .

View solution

Question 2

A curve is represented parametrically by the equations

x = f (t) = a^{I n (b^{'})} and y = g (t) = b^{- I n (a^{t})} a, b > 0 and a \neq = 1, b \neq = 1 Where t \in R .

The value of

\frac{f ( t )}{f ^{'} ( t )} \cdot \frac{f ^{''} ( - t )}{f ^{'} ( - t )} + \frac{f ( - t )}{f ^{'} ( - t )} \cdot \frac{f ^{''} ( t )}{f ^{'} ( t )} \forall t \in R

View solution

Question 3

x = a (θ - sin θ), y = a (1 + cos θ),

find

\frac{d ^{2} y}{d x ^{2}}

View solution

Question 4

Repeated roots : If equation f(x) = 0, where f(x) is a polyno- mial function, has roots

α, α, β, \dots or α

root is repreated root, then f(x) = 0 is equivalent to

(x - α)^{2} (x - β) \dots = 0,

from which we can conclude that

f (x) = 0 or 2 (x - α) [(x - β) \dots] + (x - α)^{2} [(x - β) \dots]^{'} = 0 or (x - α) [2 {(x - β) \dots} + (x - α) {(x - β) \dots}^{'}] = 0

has root

α

. Thus, if

α

root occurs twice in the, equation, then it is common in equations f(x) = 0 and f'(x) = 0. Similarly, if

α

root occurs thrice in equation, then it is common in the equations f(x)=0, f'(x)=0, and f'''(x)=0.
If x-c is a factor of order m of the polynomial f(x) of degree n

(1 < m < n)

, then x=c is a root of the polynomial [where

f^{r} (x)

represent rth derivative of f(x) w.r.t. x]

View solution

Question Text

y = e^{s i n x^{3}}

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$y = e^{s i n x^{3}}$