Basic Differentiation Rules Score 13/30 13/30 answered Question 16 Let h(v)=(2 v+3)(7 v+5) Determine the derivative of h h (v)= Determine the slope of h at v=2 h (2)= Submit All Parts

Question

StudyX AI with GPT-3.5 Turbo Model · Accepted Answer

Solution By Steps
Step 1: Product Rule
Apply the product rule: $(f \cdot g)' = f' \cdot g + f \cdot g'$.

Step 2: Find $h'(v)$
$h'(v) = (2v+3)'(7v+5) + (2v+3)(7v+5)'$.

Step 3: Derivative of $(2v+3)$
$(2v+3)' = 2$.

Step 4: Derivative of $(7v+5)$
$(7v+5)' = 7$.

Step 5: Substitute into $h'(v)$
$h'(v) = 2(7v+5) + (2v+3)7$.

Step 6: Simplify
$h'(v) = 14v + 10 + 14v + 21$.

Step 7: Final Derivative
$h'(v) = 28v + 31$.

Step 8: Find $h'(2)$
Substitute $v=2$ into $h'(v)$.

Step 9: Substitute $v=2$
$h'(2) = 28(2) + 31$.

Step 10: Calculate
$h'(2) = 56 + 31$.

Final Answer
$h'(v) = 28v + 31$.

$h'(2) = 87$.

Key Concept
Derivatives

Key Concept Explanation
Derivatives represent the rate of change of a function at a given point. In this case, the derivative of a product of two functions was found using the product rule, which states that the derivative of a product is the derivative of the first function times the second, plus the first function times the derivative of the second. The derivative at a specific point gives the slope of the function at that point.

Basic Differentiation Rules Score 13 30 13 30 answered Question 16 Let h v 2 v 3 7 v 5 Determine the derivative of h h v Determine the slope of h at v 2 h 2 Submit All Parts

Question

Solution 1

Learn More

Basic Differentiation Rules Score 13 30 13 30 answered Question 16 Let h v 2 v 3 7 v 5 Determine the derivative of h h v Determine the slope of h at v 2 h 2 Submit All Parts

Question

Solution 1

Related Answered Questions