Advertisements
Advertisements
प्रश्न
(x3 + x2 + 1) sin x
Advertisements
उत्तर
\[\text{ Let } u = x^3 + x^2 + 1; v = \sin x\]
\[\text{ Then }, u' = 3 x^2 + 2x; v' = \cos x\]
\[\text{ By product rule },\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ \left( x^3 + x^2 + 1 \right) \sin x \right] = \left( x^3 + x^2 + 1 \right) \cos x + \left( 3 x^2 + 2x \right) \sin x \]
\[\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of 99x at x = 100.
Find the derivative of x5 (3 – 6x–9).
Find the derivative of x–4 (3 – 4x–5).
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):
`(1 + 1/x)/(1- 1/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):
`(a + bsin x)/(c + dcosx)`
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 the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
x2 + x + 3
(x + 2)3
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
tan2 x
\[\sin \sqrt{2x}\]
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
ex log a + ea long x + ea log a
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x3 ex
x2 ex log x
xn loga x
\[e^x \log \sqrt{x} \tan x\]
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
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 \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
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
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
