This problem basically amounts to finding the derivative and evaluating it at the given value. We need to use a couple different techniques to find the derivative of this function but they're all fairly simple. We need the chain rule which says:

and the product rule, which is 

So, using these we can calculate our derivative.  and , so:

this equals,

and when we plug in , we get

which can be written as . 

To find the slope, you must find the derivative of the function. Remember, when taking the derivative, multiply the exponent by the coefficient and then subtract 1 from the exponent, this is known as the power rule.

Therefore, the derivative is:

.

Then, to find the slope at 1, just plug 1 into the derivative.

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The slope (m) between two points is found with the following formula:

We can apply this formula with the points we are given:

This is one of the answer choices.

The slope of a function at a given point is found by first taking the derivative of the function.

Use the power rule to find this derivative, given by:

By evaluating the derivative when  you will find the slope of the function at the point .

To find the value of the slope at , you must first find the derivative of the function since that will give us the slope. To take the derivative of a term, multiplty the exponent by the coefficient in front of the  term, and then subtract  from the exponent. Therefore, the derivative is: . Then, plug in  to get the correct slope value. .

To find the slope, you must first find the derivative. To take the derivative, multiply the exponent by the leading coefficient and then subtract 1 from the exponent. Therefore, the derivative is: . Then, plug in 2 to get the specific value: .

To find the slope, you must first find the derivative function. To take the derivative, multiply the exponent by the leading coefficient and then subtract 1 from the exponent. Therefore, the derivative is: . Then, plug in -1. .

To find the slope, you must first find the derivative of the function. To take the derivative, multiply the exponent by the coefficient in front of the x term and then subtract 1 from the exponent: . Now, plug in 1 for x to get your answer of x=5.

Find the slope of the line tangent to the curve of g(x) when x is equal to 5.

To find the slope of a tangent line, first find the derivative of the beginning functions:

Will become:

Next, simply plug in 5 everywhere we have an x and solve.

So our answer is 55548

Find the slope of the line tangent to h(x), when .

To find the slope of a tangent line, we need to find the derivative of our function:

Begin by recalling the rule for polynomial derivatives, derivative of sine, and derivative of 

Polynomials derivatives are found by decreasing our exponent by one, and then dividing by that number.

The derivative of sine is cosine

The derivative of  is 

So with that in mind, let's find h'(x)

Next, we need to find h'(0), so plug in 0 for x and simplify:

So our slope is 0 when x=0.