Advertisements
Advertisements
Question
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
Advertisements
Solution
\[ = \frac{d}{dx}\left[ log \left( x^\frac{- 1}{2} \right) \right] + 5\frac{d}{dx}\left( x^a \right) - 3\frac{d}{dx}\left( a^x \right) + \frac{d}{dx}\left( x^\frac{2}{3} \right) + 6\frac{d}{dx}\left( x^\frac{- 3}{4} \right)\]
\[ = \frac{d}{dx}\left( \frac{- 1}{2}\log x \right) + 5\frac{d}{dx}\left( x^a \right) - 3\frac{d}{dx}\left( a^x \right) + \frac{d}{dx}\left( x^\frac{2}{3} \right) + 6\frac{d}{dx}\left( x^\frac{- 3}{4} \right)\]
\[ = \frac{- 1}{2} . \frac{1}{x} + 5a x^{a - 1} - 3 a^x \log a + \frac{2}{3} x^\frac{- 1}{3} + 6\left( \frac{- 3}{4} \right) x^\frac{- 7}{4} \]
\[ = \frac{- 1}{2x} + 5a x^{a - 1} - 3 a^x \log a + \frac{2}{3} x^\frac{- 1}{3} - \frac{9}{2} x^\frac{- 7}{4} \]
\[\]
APPEARS IN
RELATED QUESTIONS
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):
`(px+ q) (r/s + s)`
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):
(ax + b)n
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):
`(sin(x + a))/ cos x`
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) = 99x at x = 100
Find the derivative of the following function at the indicated point:
\[\frac{2}{x}\]
\[\frac{1}{\sqrt{3 - x}}\]
Differentiate of the following from first principle:
sin (x + 1)
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
tan 2x
\[\tan \sqrt{x}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
xn tan x
xn loga x
\[\frac{2^x \cot x}{\sqrt{x}}\]
(x sin x + cos x) (x cos x − sin x)
(1 +x2) cos x
sin2 x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
(ax + b)n (cx + d)n
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
\[\frac{1}{a x^2 + bx + c}\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
