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Find the second derivative of $y=\sqrt{3x^2-2x+1}$ By indices $y=(3x^2-2x+1)^\frac{1}{2}$ We use chain rule to evaluate $y$.  Formula $\frac{dy}{dx}=\frac{dy}{du}\times…

Linear Approximation Of Functions Given a function $f(x)$,if $x=a$ then the linear approximation of $f(x)$ is given by $L(x)=f'(a)(x-a)+f(a)$ Examples Use Lin…

Differentials of Functions for any function $f(x)$ that is differentiable,we defined $y=f(x)$ so that $\frac{dy}{dx}=f'(x)$ and the differential is given as $dy=…

JAMB past questions on Calculus below are some of the calculus questions from the previous jamb examinations, i believe you should have basic background of calculus,we…

Definition of Analytic Functions i) A complex function $f(z)$ is said at a point $z_0$, if $f$ is differentiable not only at $z_0$ but at every point of some neighborho…

Below are few calculus  Questions which  I solved..  (1)Find the derivative of the following if: (i) 2y²=x²siny+xy³ (ii)x²y²+4xy+x-6y=2 (2)differentiate y=cos-¹(4x³-1) (…

A qoutient function is a function expressed in terms of division for exam a/b. Hence in differentiation any function expressed in terms of qoutient are usually evaluat…

Here we give a little bit more difficult example of the product formula of differentiation.. We can see clearly that the first function here (x³+2)² is not a function we…

The product rule is simple and very interesting to use.. All you need to do is to define your given functions in terms of the variables of the product formula. You fir…

Example 2: find the derivative of (3χ²+4x)⁴ Solution : we simply use chain Rule because the function is defined in terms of powers. Chain Rule formula : dy/dx= dy/…

Rule 2: the chain Rule This rule is quite simple and easy it defined by: dy/dx= dy/du × du/dx To carry out chain Rule in any given function then that function must b…

differentiation is simple  in fact we can say  it's the simplest aspect or topic of mathematics.. But to carry out differentiation we need to know the rules. Rule1:…