Advertisements
Advertisements
प्रश्न
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
Advertisements
उत्तर
\[\text{ Slope of the tangent } =f'(x)\]
\[ = \frac{d}{dx}\left( 2 x^6 + x^4 - 1 \right)\]
\[ = 2\frac{d}{dx}\left( x^6 \right) + \frac{d}{dx}\left( x^4 \right) - \frac{d}{dx}\left( 1 \right)\]
\[ = 12 x^5 + 4 x^3 \]
\[ \therefore \text{ Slope of the tangent at }x=1:\]
\[12 \left( 1 \right)^5 + 4 \left( 1 \right)^3 = 12 + 4 = 16\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
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 `2x - 3/4`
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):
`(ax + b)/(px^2 + qx + r)`
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):
`4sqrtx - 2`
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
\[\frac{1}{\sqrt{3 - x}}\]
x2 + x + 3
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
x2 ex
tan 2x
\[\sqrt{\tan x}\]
\[\sin \sqrt{2x}\]
ex log a + ea long x + ea log a
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
(x3 + x2 + 1) sin x
\[\frac{2^x \cot x}{\sqrt{x}}\]
x2 sin x log x
sin2 x
x4 (5 sin x − 3 cos x)
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{3^x}{x + \tan x}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
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:
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
