What is the derivative of 1 over X?

Answer: The derivative of 1/x is -1/x2.

What is x² 1 differentiated with respect to x?

Differentiate. By the Sum Rule, the derivative of x2−1 x 2 – 1 with respect to x x is ddx[x2]+ddx[−1] d d x [ x 2 ] + d d x [ – 1 ] .

What is the derivative of 1 /( 1 E X?

By the Sum Rule, the derivative of 1−ex 1 – e x with respect to x x is ddx[1]+ddx[−ex] d d x [ 1 ] + d d x [ – e x ] .

What is the differentiation of 1 2x?

Since 12 is constant with respect to x , the derivative of 12x 1 2 x with respect to x is 12ddx[1x] 1 2 d d x [ 1 x ] . Rewrite 1x as x−1 . Differentiate using the Power Rule which states that ddx[xn] d d x [ x n ] is nxn−1 n x n – 1 where n=−1 . Combine fractions.

What is the first principle of derivative?

According to the first principle of differentiation, the derivative of a function can be evaluated by calculating the limit \[f’\left( x \right){\text{ = }}\mathop {\lim }\limits_{h \to 0} \dfrac{{f(x + h) – f{\text{(x)}}}}{h}\] .

What is derivative Sinx?

THE DERIVATIVE of sin x is cos x. To prove that, we will use the following identity: sin A − sin B = 2 cos ½(A + B) sin ½(A − B). (Topic 20 of Trigonometry.)

What is H in derivative formula?

The value of. f(a+h)−f(a)h. is the slope of the line through the points (a,f(a)) and (a+h,f(a+h)), the so called secant line. Note that Δx=a+h−a=h and Δy=f(a+h)−f(a). The limit of the secant lines as h tends to zero is the tangent line.

How do you calculate anti – derivative?

To find the anti-derivative of a particular function, find the function on the left-hand side of the table and find the corresponding antiderivative in the right-hand side of the table. For example, if the antiderivative of cos(x) is required, the table shows that the anti-derivative is sin(x) + c.

What is the chain rule of derivatives?

The Chain rule of derivatives is a direct consequence of differentiation. Chain Rule in Derivatives: The Chain rule is a rule in calculus for differentiating the compositions of two or more functions. All functions are functions of real numbers that return real values.

What are basic derivatives?

At its most basic, a financial derivative is a contract between two parties that specifies conditions under which payments are made between two parties. Derivatives are “derived” from underlying assets such as stocks, contracts, swaps, or even, as we now know, measurable events such as weather.

What is product rule of derivatives?

In calculus, the product rule is a formula used to find the derivatives of products of two or more functions.