Solved example of chain rule of differentiation
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 $3$ and $-1$
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
The derivative of a sum of two or more functions is the sum of the derivatives of each function
The derivative of a function multiplied by a constant ($3$) is equal to the constant times the derivative of the function
The derivative of the linear function is equal to $1$
The derivative of the linear function times a constant, is equal to the constant
The derivative of a function multiplied by a constant ($-2$) 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 $-2$ 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 $f'(x) = nx^{n-1}$
Factor the polynomial $\left(3x-2x^2\right)$ by it's GCF: $x$
Simplifying
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