Calculus 1 : How to find solutions to differential equations

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #31 : Differential Equations

Differentiate the expression.

Possible Answers:

Correct answer:

Explanation:

We will use the fact that  to differentiate. Let  and . Substituing our values we can see the derivative will be .

Example Question #21 : Solutions To Differential Equations

Differentiate the expression.

Possible Answers:

Correct answer:

Explanation:

Using the product rule, we determine the derivative of 
Let  and . We can see that  and .

Plugging in our values into the product rule formula, we are left with the final derivative of .

Example Question #33 : Differential Equations

Differentiate the value.

Possible Answers:

Correct answer:

Explanation:

According to the power rule, whenever we differentiate a constant value it will reduce to zero. Since the only term of our function is a constant, we can only differentiate  .

Example Question #21 : How To Find Solutions To Differential Equations

Find .

Possible Answers:

Correct answer:

Explanation:

Using the chain rule, we will differentiate the exponent of our exponential function, and then multiply our original function. Differentiating our exponent with the power rule will yield . Using the chain rule we will multiply this by our original function resulting in .

Example Question #22 : Solutions To Differential Equations

Find .

Possible Answers:

Correct answer:

Explanation:

Using the power rule, we can differentiate our first term reducing the power by one and multiplying our term by the original power. , will thus become . The second term is a constant value, so according to the power rule this term will become .

Example Question #23 : Solutions To Differential Equations

Differentiate the logarithm. 

Possible Answers:

Correct answer:

Explanation:

Using the chain rule, we will determine the derivative of our function will be .

The derivative of the log function is , and our second term of the chain rule will cancel out .

Thus our derivative will be .

Example Question #1331 : Functions

Differentiate the polynomial.

Possible Answers:

Correct answer:

Explanation:

Using the power rule, we can differentiate our first term reducing the power by one and multiplying our term by the original power. , will thus become . The second term , will thus become . The last term is , will reduce to .

Example Question #281 : Equations

Find .

Possible Answers:

Correct answer:

Explanation:

According to the quotient rule, the derivative of ,

.

We will let  and 
Plugging all of our values into the quotient rule formula we come to a final solution of :

Example Question #31 : Differential Equations

Differentiate the polynomial.

Possible Answers:

Correct answer:

Explanation:

Using the power rule, we can differentiate our first term reducing the power by one and multiplying our term by the original power. , will thus become . The second term , will thus become .

Example Question #24 : Solutions To Differential Equations

Solve the differential equation:  

Possible Answers:

Correct answer:

Explanation:

Rewrite  by multiply the  on both sides, and dividing  on both sides of the equation.

Integrate both sides of the equation and solve for y.

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