Advertisements
Advertisements
प्रश्न
3x + x3 + 33
Advertisements
उत्तर
\[\frac{d}{dx}\left( 3^x + x^3 + 3^3 \right)\]
\[ = \frac{d}{dx}\left( 3^x \right) + \frac{d}{dx}\left( x^3 \right) + \frac{d}{dx}\left( 3^3 \right)\]
\[ = 3^x \log 3 + 3 x^2 + 0\]
\[ = 3^x \log 3 + 3 x^2\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of 99x at x = 100.
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
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)
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) = 3x at x = 2
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan (2x + 1)
\[\sqrt{\tan x}\]
(2x2 + 1) (3x + 2)
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x3 ex
x2 sin x log x
(x sin x + cos x ) (ex + x2 log x)
(1 − 2 tan x) (5 + 4 sin x)
(1 +x2) cos x
x3 ex cos x
(2x2 − 3) sin x
(ax + b)n (cx + d)n
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Mark the correct alternative in of the following:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
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 \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
`(a + b sin x)/(c + d cos x)`
