Advertisements
Advertisements
प्रश्न
Find the derivative of (5x3 + 3x – 1) (x – 1).
Advertisements
उत्तर
Let f (x) = (5x3 + 3x – 1) (x – 1) ...(1)
Differentiating (1) with respect to x, we get
f'(x) = (5x3 + 3x - 1) (x - 1) + (5x3 + 3x - 1)(x - 1)
= f'(x) = (5.3x2 + 3 - 0) (x - 1) + (5x3 + 3x - 1) (1 - 0)
= (15x2 + 3) (x - 1) + (5x3 + 3x -1) (1)
= 15x3 + 3x - 15x2 - 3 + 5x3 + 3x - 1
∴ f'(x) = 20x3 - 15x2 + 6x - 4
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–3 (5 + 3x).
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 (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):
cosec x cot 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)
Find the derivative of f (x) x at x = 1
\[\frac{x^2 - 1}{x}\]
k xn
(x + 2)3
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
tan 2x
\[\tan \sqrt{x}\]
\[\tan \sqrt{x}\]
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
cos (x + a)
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x3 sin x
(1 +x2) cos x
x−4 (3 − 4x−5)
x−3 (5 + 3x)
\[\frac{x}{1 + \tan x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
Find the derivative of x2 cosx.
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
