Find the derivative of . x^5(3-6x^ -9 ) - Vidyadip

Question

Find the derivative of . $\text{x}^5(3-6\text{x}^{-9})$

✓

Answer

Let $\text{f}(\text{x})=\text{x}^5(3-6\text{x}^{-9})$ By Leibnitz product rule, $\text{f}'\big(\text{x})=\text{x}^5\frac{\text{d}}{\text{dx}}\big(3-6\text{x}^{-9}\big)+\big(3-6\text{x}^{-9}\big)\frac{\text{d}}{\text{dx}}\big(\text{x}^5\big)$ $=\text{x}^5\big\{0-6(-9)\text{x}^{-9-1}\big\}+(3-6\text{x}^{-9})(5\text{x}^4)$ $=\text{x}^5(54\text{x}^{-10})+15\text{x}^4-30\text{x}^{-5}$ $=54\text{x}^{-5}+15\text{x}^4-30\text{x}^{-5}$ $=24\text{x}^{-5}+15\text{x}^4$ $=15\text{x}^4+\frac{24}{\text{x}^5}$

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 "(Each question 2 marks)" from LIMITS AND DERIVATIVES→LIMITS AND DERIVATIVES — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Assuming that straight lines work as the plane mirror for a point, find the image of the point (1, 2) in the line x – 3y + 4 = 0

Show the of the following progression is G.P. Also, find the common ratio in case:$\text{a}\frac{3\text{a}^2}{4},\frac{9\text{a}^3}{16},\cdots$

Find the coordinates of focus, axis, the equation of directrix and latus rectum of parabola $\mathrm{y}^2=8 \mathrm{x}$.

How many terms are there in the A.P. 7, 10, 13, ...43?

Find the number of permutations of the letters of the word ALLAHABAD.

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B= {2, 3, 5, 7}, verify that: (A $\cap$ B)' = A' $\cup$ B'.

Find the centre and the radius of the circle: $x^2+y^2+8 x+10 y-8=0$

What is the value of y so that the line through (3, y) and (2, 7) is parallel to the line through (-1, 4) and (0, 6)?

Find the value of p so that three lines 3x + y - 2 = 0, px + 2y - 3 = 0 and 2x - y - 3 = 0 may intersect at one point.

Find the equation of the line perpendicular to x-axis and having intercept -2 on x-axis.