If x=4z^2+5,y=6z^2+7z+3find d^2y dx^2 . - Vidyadip

Question

If $\text{x}=4\text{z}^2+5,\text{y}=6\text{z}^2+7\text{z}+3$find $\frac{\text{d}^2\text{y}}{\text{dx}^2}.$

✓

Answer

Here,
$\text{x}=4\text{z}^2+5,\text{y}=6\text{z}^2+7\text{z}+3$
Differentiating w.r.t.x, we get
$\frac{\text{dx}}{\text{dz}}=8\text{z}\ \text{and}\ \frac{\text{dy}}{\text{dz}}=12\text{z}+7$
$\therefore\frac{\text{dy}}{\text{dx}}=\frac{12\text{z}+7}{8\text{z}}$
Differentiating w.r.t.x, we get
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{12\times8\text{z}-8(12\text{z}+7)}{64\text{z}^2}\times\frac{\text{dz}}{\text{dx}}$
$=\frac{96\text{z}-96\text{z}-56}{512\text{z}^3}=\frac{-7}{64\text{z}^3}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Higher Order Derivatives→Higher Order Derivatives — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Write a value of $\int\frac{\sin2\text{x}}{\text{a}^2\sin^2\text{x}+\text{b}^2\cos^2\text{x}}\text{ dx}$

Evaluate the following definite integrals:
$\int_{1}^\limits{\text{e}}\frac{\log\text{x}}{\text{x}}\text{ dx}$

Evaluate the following integrals:
$\int^\limits4_{-4}|\text{x}+2|\text{dx}$

If f(x) = |x - 2| write whether f(2) exists or not.

Evaluate the following integrals:
$\int\frac{\text{x}^2}{\text{x}^6+\text{a}^6}\text{dx}$

Find $\frac{1}{2}\left(\mathrm{~A}+\mathrm{A}^{\prime}\right)$ and $\frac{1}{2}\left(\mathrm{~A}-\mathrm{A}^{\prime}\right)$ when $A=\left[\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right]$.

Find the volume of the parallelopiped whose coterminous edges are represented by the vectors:
$\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}},\vec{\text{b}}=\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}},\vec{\text{c}}=3\hat{\text{i}}-\hat{\text{j}}-2\hat{\text{k}}$

Examine the continuity of function.$
f(x)=\left\{\begin{array}{ll}
1+x, & x \leq 3 \\
7-x, & x>3
\end{array} \text { at } x=3\right.
$

Check the commutativity and associativity of the following binary operations:
'*' on Q defined by a * b = ab + 1 for all a, b ∈ Q.

Evaluate the following integrals:
$\int\frac{\log\text{x}^2}{\text{x}}\text{dx}$