Question
Write the chain rule of differentiation.
✓
Answer
| If $y$ is a differentiable function of $u$ and $u$ is a differentiable function of $x,$ then $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$ |
| This rule is known as Chain Rule, Which used in differentiation of composite function |
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The data about sugar production of a sugar manufacturing company from the year $2008$ to $2015$ are as follows. Prepare index number by fixed base method from these data by taking average production of the years $2009, 2010$ and $2011$ as the production of the base year.
→In each of the following $Z$ is a standard normal variate. Using the table of area under normal curve obtain the probabilities of the following: $($Diagram is necessary.$)$
$(1) P[0 \leq Z \leq 2.3] $
$(2) P[0 \leq Z \leq 0.75] $
$(3) P[-1.52 \leq Z \leq 01] $
$(4) P[-0.30 \leq Z \leq 01] $
$(5) P[1.48 \leq Z \leq 2.35] $
$(6) P[0.62 \leq Z \leq 1.931] $
$(7) P[-1.1 \leq Z \leq-0.72] $
$(8) P[-2.45 \leq Z \leq 1.1]$
→$(1) P[0 \leq Z \leq 2.3] $
$(2) P[0 \leq Z \leq 0.75] $
$(3) P[-1.52 \leq Z \leq 01] $
$(4) P[-0.30 \leq Z \leq 01] $
$(5) P[1.48 \leq Z \leq 2.35] $
$(6) P[0.62 \leq Z \leq 1.931] $
$(7) P[-1.1 \leq Z \leq-0.72] $
$(8) P[-2.45 \leq Z \leq 1.1]$
The probability that the price of potato rises in the vegetable market during festive days in $0.8$. The probability that the price of onion rises is $0.7 .$ The probability of rise in price of both potato and onion is $0.6$ Find the probability of rise in price of at least one of the two, potato and onion.
→If $\mathrm{L}_{\mathrm{L}}=80$ and $\mathrm{I}_F=100$ find $\mathrm{I}_p$.
→Define elasticity of demand and write the formula for
finding elasticity of demand from demand function.
finding elasticity of demand from demand function.
Find $\frac{d^2 y}{d x^2}$ if $y =\sqrt{x}+\frac{1}{\sqrt{x}}$
→From $12$ pairs of observations of variables $X$ and $Y$, we get Cov $(x, y)=$ $-240, S_{x}=15$ and $S_{y}=20$ calculate r( $(x, y)$.
→State multiplication and division working rule of limit.
The following results are obtained while studying the annual income $($thousand $₹ )$ and annual saving $($thousand $₹)$ of a particular family. $\bar{y}=60$, variance of $X=144$, covariance $(x, y)=300$ and intercept $=-54$. Find the mean of $X$.
→Express the following in modulus and neighbourhood form: $1.998 < x < 2.002$
→