Download App

Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability2 Marks
Question
Find the second-order derivatives of the function $x^{20}$
✓

Answer

Let us take $y = x^{20}$
Now,
$\frac{d y}{d x}=\frac{d}{d x}(x^{20})$
$= 20 x^{19}$
Therefore,
$\frac{d^{2} y}{d x^{2}}=\frac{d}{d x}\left(20 x^{19}\right)=20 \frac{d}{d x}{\left(x^{19}\right)}  = 20 \times 19 \times x^{18}$
$= 380 x^{18}$

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 "2 Marks Questions" from Continuity and Differentiability→Continuity and Differentiability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $A=\left[\begin{array}{cc} {\sin \alpha} & {\cos \alpha} \\ {-\cos \alpha} & {\sin \alpha} \end{array}\right]$, then verify that A′ A = I
→
Find the value of k so that the lines x = -y = kz and x - 2 = 2y + 1 = -z + 1 are perpendicular to each other.
→
Let $A$ and $B$ be two independent events such that $P(A) = p_1$ and $P(B) = p_2.$ Describe in words the events whose probabilities are:
$p_1p_{2}.$
→
If $\vec{\text{a}}$ is a vector and m is a scalar such that m $\vec{\text{a}}=\vec0$, then what are the alternatives for m and $\vec{\text{a}}$?
→
If the binary operation o is defined by a o b = a + b - ab on the set Q - {-1} of all rational numbers other than 1, shown that o is commutative on Q - [1].
→
Write the position vector of a point dividing the line segment joining points A and B with position vectors $\vec{\text{a}}\text{ and }\vec{\text{b}}$ externally in the ratio 1 : 4, where $\vec{\text{a}}=2\hat{\text{i}}+3\hat{\text{j}}+4\hat{\text{k}}$ and $\vec{\text{b}}=-\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$.
→
Let $A$ be a $3 \times 3$ square matrix, such that $A ($adj $A) = 2I,$ where $I$ is the identity matrix. Write the value of $|$adj $A|.$
→
Let A and B be matrices of orders 3×2 and 2×4 respectively. Write the order of matrix AB. 
→
If $A$ and $B$ are square matrices of the same order, explain, why in general:
$(A − B)^2 \neq A^2 − 2AB + B^2$
→
By using the properties of definite integrals, evaluate the integral $\int\limits_0^{2\pi } {{{\cos }^5}x} dx$
→