Solved example of inverse trigonometric functions differentiation
Taking the derivative of arcsine
Multiplying the fraction by $\frac{d}{dx}\left(4x^2\right)$
Taking the derivative of arcsine
The power of a product is equal to the product of it's factors raised to the same power
The derivative of a function multiplied by a constant ($4$) is equal to the constant times the derivative of the function
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
Subtract the values $2$ and $-1$
Multiply $4$ times $2$
Any expression to the power of $1$ is equal to that same expression
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
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