Advertisements
Advertisements
Question
Find the derivative of x–3 (5 + 3x).
Advertisements
Solution
Let f (x) = x– 3 (5 + 3x) ...(1)
Differentiating (1) with respect to x, we get
f'(x) = (x-3) (5 + 3x) + (x-3) (5 + 3x)
= f'(x) = (-3) x-3-1 (5 + 3x) + (x-3) (0 + 3)
= `3x-4 (5 + 3x) + x-3. (3)
= -15x-4 + 9x-3 + 3x-3
= -15x-4 - 6x-3
= `(-15)/x^4 - 6/x^3`
∴ f'(x) = `(-3)/ x^4 (5 + 2x)`
APPEARS IN
RELATED QUESTIONS
Find the derivative of x2 – 2 at x = 10.
Find the derivative of (5x3 + 3x – 1) (x – 1).
Find the derivative of `2/(x + 1) - x^2/(3x -1)`.
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`(ax + b)/(px^2 + qx + r)`
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`4sqrtx - 2`
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`(sec x - 1)/(sec x + 1)`
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of the following function at the indicated point:
\[\frac{x + 2}{3x + 5}\]
(x2 + 1) (x − 5)
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
tan2 x
\[\tan \sqrt{x}\]
3x + x3 + 33
(2x2 + 1) (3x + 2)
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
xn loga x
x2 sin x log x
(x sin x + cos x) (x cos x − sin x)
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same.
(ax + b) (a + d)2
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
Find the derivative of x2 cosx.
(ax2 + cot x)(p + q cos x)
