Final Answer
Step-by-step Solution
Problem to solve:
Solving method
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\left(2x+1\right)^5$ and $g=\left(x^4-3\right)^6$
Subtract the values $5$ and $-1$
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
Subtract the values $5$ and $-1$
Subtract the values $6$ 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 functions is the sum of the derivatives of each function
$x+0=x$, where $x$ is any expression
The derivative of the constant function ($1$) is equal to zero
Multiply $5$ times $2$
The derivative of a function multiplied by a constant ($2$) 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 sum of two functions is the sum of the derivatives of each function
$x+0=x$, where $x$ is any expression
$x+0=x$, where $x$ is any expression
The derivative of the constant function ($-3$) is equal to zero
Subtract the values $4$ and $-1$
Multiply $6$ times $4$
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$