Advertisements
Advertisements
प्रश्न
x5 ex + x6 log x
Advertisements
उत्तर
\[ = x^5 \frac{d}{dx}\left( e^x \right) + e^x \frac{d}{dx}\left( x^5 \right) + x^6 \frac{d}{dx}\left( \log x \right) + \log x \frac{d}{dx}\left( x^6 \right)\]
\[ = x^5 e^x + e^x \left( 5 x^4 \right) + x^6 . \frac{1}{x} + \log x\left( 6 x^5 \right)\]
\[ = x^5 e^x + e^x \left( 5 x^4 \right) + x^5 + \log x\left( 6 x^5 \right)\]
\[ = x^4 \left( x e^x + 5 e^x + x + 6x \log x \right)\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x5 (3 – 6x–9).
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):
(x + a)
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^2 +qx + r)/(ax +b)`
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):
`a/x^4 = b/x^2 + cos x`
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
k xn
\[\frac{1}{\sqrt{3 - x}}\]
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[3^{x^2}\]
\[\cos \sqrt{x}\]
\[\tan \sqrt{x}\]
ex log a + ea long x + ea log a
(2x2 + 1) (3x + 2)
\[\frac{2 x^2 + 3x + 4}{x}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
x2 ex log x
xn loga x
(1 +x2) cos x
\[e^x \log \sqrt{x} \tan x\]
x−3 (5 + 3x)
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
Mark the correct alternative in of the following:
If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
(ax2 + cot x)(p + q cos x)
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
