Find the derivative of the following function: f(x)= 10x-3/5x +6x
Could you please insert parentheses to clarify the question?
10x-3/5x+6x
could mean
(10x-3)/(5x+6x) [??]
10x -(3/5x) + 6x [??]
[(10x-3)/5x] +6x [??}
etc.
There are no parentheses, that's what is confusing me also. The questions is exactly as written above.
Parentheses are implicit when it is printed in fraction form.
If it is printed as a fraction, your post is linearizing it (put on a single line) and it is necessary to insert parentheses around all numerators or denominators which contain more than one term.
To find the derivative of a function, we can use the power rule and the quotient rule.
Step 1: Simplify the expression inside the function.
In this case, we have f(x) = (10x - 3)/(5x + 6x).
Combining like terms, we have f(x) = (10x - 3)/(11x).
Step 2: Apply the quotient rule to find the derivative of f(x).
The quotient rule states that if we have a function h(x) = u(x)/v(x), where u(x) and v(x) are differentiable functions, then the derivative of h(x) is given by:
h'(x) = (u'(x)v(x) - u(x)v'(x))/[v(x)]^2.
In our case, u(x) = (10x - 3) and v(x) = 11x.
Applying the quotient rule, we have:
f'(x) = [(u'(x)v(x) - u(x)v'(x))/(v(x))^2]
= [(10 * 11x - (10x - 3) * 11)/(11x)^2]
= [110x - (110x - 33)]/(11x)^2
= [33]/(11x)^2
= 33/(11x)^2.
Therefore, the derivative of the function f(x) = 10x-3/(5x + 6x) is f'(x) = 33/(11x)^2.