Advertisements
Advertisements
Question
3x + x3 + 33
Advertisements
Solution
\[\frac{d}{dx}\left( 3^x + x^3 + 3^3 \right)\]
\[ = \frac{d}{dx}\left( 3^x \right) + \frac{d}{dx}\left( x^3 \right) + \frac{d}{dx}\left( 3^3 \right)\]
\[ = 3^x \log 3 + 3 x^2 + 0\]
\[ = 3^x \log 3 + 3 x^2\]
APPEARS IN
RELATED QUESTIONS
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):
`(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)/(cx + d)`
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):
`1/(ax^2 + bx + c)`
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):
`cos x/(1 + sin x)`
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):
sinn x
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):
x4 (5 sin x – 3 cos x)
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 2}{3x + 5}\]
\[\frac{1}{\sqrt{3 - x}}\]
Differentiate of the following from first principle:
e3x
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
(2x2 + 1) (3x + 2)
2 sec x + 3 cot x − 4 tan x
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
x3 sin x
x2 ex log x
xn tan x
(x3 + x2 + 1) sin x
x3 ex cos x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
(ax + b)n (cx + d)n
\[\frac{x}{1 + \tan x}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
Find the derivative of 2x4 + x.
