Calculus Examples

Find dy/dx y = square root of sin(3x)^2+x
Step 1
Use to rewrite as .
Step 2
Differentiate both sides of the equation.
Step 3
The derivative of with respect to is .
Step 4
Differentiate the right side of the equation.
Tap for more steps...
Step 4.1
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 4.1.1
To apply the Chain Rule, set as .
Step 4.1.2
Differentiate using the Power Rule which states that is where .
Step 4.1.3
Replace all occurrences of with .
Step 4.2
To write as a fraction with a common denominator, multiply by .
Step 4.3
Combine and .
Step 4.4
Combine the numerators over the common denominator.
Step 4.5
Simplify the numerator.
Tap for more steps...
Step 4.5.1
Multiply by .
Step 4.5.2
Subtract from .
Step 4.6
Differentiate using the Sum Rule.
Tap for more steps...
Step 4.6.1
Move the negative in front of the fraction.
Step 4.6.2
Combine fractions.
Tap for more steps...
Step 4.6.2.1
Combine and .
Step 4.6.2.2
Move to the denominator using the negative exponent rule .
Step 4.6.3
By the Sum Rule, the derivative of with respect to is .
Step 4.7
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 4.7.1
To apply the Chain Rule, set as .
Step 4.7.2
Differentiate using the Power Rule which states that is where .
Step 4.7.3
Replace all occurrences of with .
Step 4.8
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 4.8.1
To apply the Chain Rule, set as .
Step 4.8.2
The derivative of with respect to is .
Step 4.8.3
Replace all occurrences of with .
Step 4.9
Differentiate.
Tap for more steps...
Step 4.9.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.9.2
Multiply by .
Step 4.9.3
Differentiate using the Power Rule which states that is where .
Step 4.9.4
Multiply by .
Step 4.9.5
Differentiate using the Power Rule which states that is where .
Step 4.9.6
Reorder the factors of .
Step 5
Reform the equation by setting the left side equal to the right side.
Step 6
Replace with .