This is of the form y' = u(x)/v(x) Using the quotient rule of differentiation, we know that d/dx(u/v) = (v.u'- u.v')/ v2 v = 1 + tan x and u = x v' = sec2x and u' = 1 ddx(x1+tanx)=(1+tanx)−(xsec2x)(1+tanx)2=1+tanx−xsec2x(1+tanx)2ddx(x1+tan...
Implicit differentiationis the process of differentiating animplicit function.An implicit function is a function that can be expressed as f(x, y) = 0. i.e., it cannot be easily solved for 'y' (or) it cannot be easily got into the form of y = f(x). Let us consider an example of...
(sec x)' = sec x tan x (cosec x)' = -cosec x cot x (cot x)' = -cosec2xSteps of Logarithm DifferentiationLogarithm Differentiation is the shortcut which helps in differentiating without using the product rule.If we have to differentiate the above function then we don’t need to multi...
Then, use the Quotient Rule, which finds the derivative of a quotient with both a differentiable numerator and denominator, like in sin(x) / cos(x). Lastly, the result from the quotient rule can be written more cleanly by using the identity that 1 / cos(x) = sec(x). Is tan(x) ...
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The power formula of the differentiation is:ddx[xn]=nxn−1for all real values ofn. Differentiation of the trigonometric function is:ddx[cotx]=−csc2x Answer and Explanation:1 Given: x3=coty Take the derivative of the given equation with respect tox ...
\(\therefore \frac{d}{{dx}}(\tan x) = {\sec ^2}x\) Solved Examples Q.1. Differentiate \(\sqrt {2x + 3} \) with respect to \(x\) from the first principle. Ans:Given: \(f(x) = \sqrt {2x + 3} \) \( \Rightarrow f(x + h) = \sqrt {2(x + h) + 3} \) ...
Find the derivative of the following function below: g(x) = (3x^5 + 5x^4 - 4x^3)/(x^4). Differentiate the following. (Do not simplify the expressions after applying differentiation rules). f (t) = e^sec (2 t) + ln (2 t^2 + 5) ...
1. Multiple Choice 30 sec 12 pts Find the derivative of f(x) = 2x2+3. 4x 4x2 3 4x+3 2. Multiple Choice 45 sec 12 pts Differentiate y= 12x-2 24x-1 -24x-3 -24x-1 6x-3 3. Multiple Choice 30 sec 12 pts Find the derivative of the given equationf(x) = ...
Find \frac{dy}{dx} by implicit differentiation sec (xy) = 9y. Find d y d x by implicit differentiation: e y + x 2 = 10 Find \frac{dy}{dx} by Implicit differentiation. Tan^-1(2x^2y) = x + 4xy^2 y' = Find y' by implicit differentiation. e^{\frac{...