Differentiate sin²x
We use the chain rule and the power rule of differentiation:
(sin x)²
= 2(sin x)(cos x)
= 2sin x cos x
Therefore: d/dx (sin²x) = 2sin x cos x
To differentiate sin²x, we can use the chain rule.
Step 1: Write down the function to differentiate: f(x) = sin²x.
Step 2: Apply the power rule. According to the power rule, the derivative of xⁿ with respect to x is n*x^(n-1). In this case, the exponent is 2, so we have to bring down the exponent and multiply it by the derivative of the base, sin(x).
So, the derivative of sin²x with respect to x is:
f'(x) = 2*sin(x) * cos(x).
Therefore, the differentiation of sin²x is 2*sin(x)*cos(x).