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VashaNatasha [74]
3 years ago
8

Find the derivative of f(x) = 9x + 5 at x = 7.

Mathematics
2 answers:
Sergeeva-Olga [200]3 years ago
8 0
The derivative of a variable raised to exponent of n, x^n is equal to the product of n and x raised to exponent of n-1.
                                   d(x^n) = (n)(x^n-1)
So, from the given
                                 d(9x + 5) = (1)(9x^1-0)  + 5(0)
                                                = 9
The given value of x is irrelevant to this item because the derivative does not contain any variable x. 
Inessa [10]3 years ago
7 0
<h2>Answer:</h2>

The derivative of f(x) = 9x + 5 at x = 7 is:

                  f'(7)=9

<h2>Step-by-step explanation:</h2>

The derivative of a function is the rate of change of the dependent variable i.e. y=f(x) with respect to the independent variable i.e. x.

The derivative of the function f(x) is given by:

f'(x)=\dfrac{df}{dx}

Now, we know that:

\dfrac{d}{dx}x=1\\\\\\and\\\\\\\dfrac{d}{dx}c=0

where c is a constant term.

Here we have the function f(x) as:

f(x)=9x+5

Hence,

\dfrac{d}{dx}f(x)=\dfrac{d}{dx}(9x)+\dfrac{d}{dx}5\\\\i.e.\\\\\dfrac{d}{dx}f(x)=9\dfrac{d}{dx}x+0\\\\\dfrac{d}{dx}f(x)=9

i.e.  f'(x)=9

Also, when x =7 we have:

f'(7)=9

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