Differentiate the following functions with respect to x: ( ^ -1 x… - Vidyadip

Question

Differentiate the following functions with respect to x:
$\big(\sin^{-1}\text{x}^4\big)^4$

✓

Answer

Consider $\text{y}=\big(\sin^{-1}\text{x}^4\big)^4$
Differentiate it with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\big(\sin^{-1}\text{x}^4\big)^4$
$=4\big(\sin^{-1}\text{x}^4\big)\frac{\text{d}}{\text{dx}}\big(\sin^{-1}\text{x}^4\big)$
[Using chain rule]
$=4\big(\sin^{-1}\text{x}^4\big)^3\frac{1}{\sqrt{1-\big(\text{x}^4\big)^2}}\frac{\text{d}}{\text{dx}}\big(\text{x}^4\big)$
$=4\big(\sin^{-1}\text{x}^4\big)^3\frac{4\text{x}^3}{\sqrt{1-\text{x}^8}}$
$=\frac{16\text{x}^3\big(\sin^{-1}\text{x}^4\big)^3}{\sqrt{1-\text{x}^8}}$
Hence, the solution is, $\frac{\text{d}}{\text{dx}}\big(\sin^{-1}\text{x}^4\big)=\frac{16\text{x}^3\big(\sin^{-1}\text{x}^4\big)^3}{\sqrt{1-\text{x}^8}}$

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 "5 Marks Questions" from Differentiation→Differentiation — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{A}=\begin{bmatrix}2&-2\\4&2\\-5&1\end{bmatrix},\text{ B}=\begin{bmatrix}8&0\\4&-2\\3&6\end{bmatrix},$ find matrix X such that 2A + 3X = 5B.

Without expanding, show that the values of the following determinant are zero: $\begin{vmatrix}1^2&2^2&3^2&4^2\\2^2&3^2&4^2&5^2\\3^2&4^2&5^2&6^2\\4^2&5^2&6^2&7^2\end{vmatrix}$

Find the equations of the tangent and the normal to the following curves at the indicated points.
$\text{x}=\text{at}^2,\text{y}=2\text{at at}\text{ t}=1$

A wholesale dealer deals in two kinds, $A$ and $B ($say$)$ of mixture of nuts. Each $\ kg$ of mixture $A$ contains $60$ grams of almonds$, 30$ grams of cashew nuts and $30$ grams of hazel nuts. Each $\ kg$ of mixture $B$ contains $30$ grams of almonds, $60$ grams of cashew nuts and $180$ grams of hazel nuts. The remainder of both mixtures is per nuts. The dealer is contemplating to use mixtures $A$ and $B$ to make a bag which will contain at least $240$ grams of almonds, $300$ grams of cashew nuts and $540$ grams of hazel nuts. Mixture A costs $Rs. 8$ per $\ kg. $and mixture $B$ costs $Rs. 12$ per $\ kg.$ Assuming that mixtures $A$ and $B$ are uniform, use graphical method to determine the number of $\ kg.$ of each mixture which he should use to minimise the cost of the bag.

Solve the following differential equation:
$(\text{x}+\text{y})^2\frac{\text{dy}}{\text{dx}} = 1$

Solve the following differential equations:$\text{cosec x}\log\text{y}\frac{\text{dy}}{\text{dx}}+\text{x}^2\text{y}^2=0$

Evaluate the following integrals:
$\int_{1}^\limits{2}\frac{1}{\text{x}\big(1+\log\text{x}\big)^2}\text{ dx}$

A manufacturer of patent medicines is preparing a production plan on medicines, $A$ and $B.$ There are sufficient raw materials available to make $20000$ bottles of $A$ and $40000$ bottles of $B,$ but there are only $45000$ bottles into which either of the medicines can be put. Further, it takes $3$ hours to prepare enough material to fill $1000$ bottles of $A,$ it takes $1$ hour to prepare enough material to fill $1000$ bottles of $B$ and there are $66$ hours available for this operation. The profit is $Rs. 8$ per bottle for $A$ and $Rs. 7$ per bottle for $B.$ How should the manufacturer schedule his production in order to maximize his profit?

Find the equation of the plane passing through the point (2, 3, 1), given that the direction ratios of the normal to the plane are proportional to 5, 3, 2.

A couple has two children. Find the probability that both the children are,

Males, if it is known that at least one of the children is male.
Females, if it is known that the elder child is a female.