What is the differentiation of sin x 2?

We are given a trigonometric function of the sine of the algebraic function raised to the power 2. First, we will find the derivative of the trigonometric function and then the derivative of the algebraic function. Therefore, the derivative of \[y = \sin {x^2}\] is\[2x\cos {x^2}\].

What is the differentiation of X square sin x?

Hence, the derivative of y=(x2)(sinx) is y’=2xsinx+x2cosx . Hopefully this helps!

Is sin x 2 the same as sin 2x?

Originally Answered: Is sin^2x the same as (sinx) ^2 or sin(x^2)? Yes sin^2x and (sinx)^2 is same.

How do you differentiate trigonometric functions?

Trigonometric Function Differentiation

1. If f( x) = sin x, then f′( x) = cos x.
2. If f( x) = cos x, then f′( x) = −sin x.
3. If f( x) = tan x, then f′( x) = sec 2 x.
4. If f( x) = cot x, then f′( x) = −csc 2 x.
5. If f( x) = sec x, then f′( x) = sec x tan x.
6. If f( x) = csc x, then f′( x) = −csc x cot x.

Is it sin 2 x or sin x 2?

Sin x^2 is the “sine of (x-squared)”,so it is an ordinary sine function. Sin^2 x is “sine-squared of x” which is a different function from the sine function.

What is sin 2 the same as?

sin2(x)=(sin(x))2 “The square of the sine of x.” sin(x2) “The sine of x2.” sin−1(x)=arcsin(x) “The inverse sine of x. That is, if y=sin−1(x), then sin(y)=x.”

How do you differentiate (X2)(sin x)?

How do you differentiate (x2)(sin x)? By using the product rule. Let f (x) = (x2)(sinx), then f (x) = g(x) ×h(x). The derivative of h(x) or sinx is h'(x) = cosx. Hence, the derivative of y = (x2)(sinx) is y’ = 2xsinx +x2cosx. Hopefully this helps!

What is the derivative of f(x) = x2?

Let f (x) = x2 and g(x) = ex. Since we have a product of functions, the derivative can be found with the Product Rule From some basic derivatives, we know f ‘(x) = 2x and g'(x) = ex.

What is the rule for differentiating constant functions?

The rule for differentiating constant functions and the power rule are explicit differentiation rules. The following rules tell us how to find derivatives of combinations of functions in terms of the derivatives of their constituent parts. In each case, we assume that f ‘ (x) and g’ (x) exist and A and B are constants.

What is the rule for differentiation with n = 1/2?

Hence, with n = 1/2 in the power rule, The rule for differentiating constant functions and the power rule are explicit differentiation rules. The following rules tell us how to find derivatives of combinations of functions in terms of the derivatives of their constituent parts.