Calculus Examples

Find the Derivative - d/dx f(x) = square root of x+ square root of x
Step 1
Apply basic rules of exponents.
Tap for more steps...
Step 1.1
Use to rewrite as .
Step 1.2
Use to rewrite as .
Step 2
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Combine and .
Step 5
Combine the numerators over the common denominator.
Step 6
Simplify the numerator.
Tap for more steps...
Step 6.1
Multiply by .
Step 6.2
Subtract from .
Step 7
Combine fractions.
Tap for more steps...
Step 7.1
Move the negative in front of the fraction.
Step 7.2
Combine and .
Step 7.3
Move to the denominator using the negative exponent rule .
Step 8
By the Sum Rule, the derivative of with respect to is .
Step 9
Differentiate using the Power Rule which states that is where .
Step 10
Differentiate using the Power Rule which states that is where .
Step 11
To write as a fraction with a common denominator, multiply by .
Step 12
Combine and .
Step 13
Combine the numerators over the common denominator.
Step 14
Simplify the numerator.
Tap for more steps...
Step 14.1
Multiply by .
Step 14.2
Subtract from .
Step 15
Move the negative in front of the fraction.
Step 16
Combine and .
Step 17
Move to the denominator using the negative exponent rule .
Step 18
Simplify.
Tap for more steps...
Step 18.1
Reorder the factors of .
Step 18.2
Multiply by .
Step 18.3
Simplify the numerator.
Tap for more steps...
Step 18.3.1
Write as a fraction with a common denominator.
Step 18.3.2
Combine the numerators over the common denominator.
Step 18.4
Multiply the numerator by the reciprocal of the denominator.
Step 18.5
Multiply .
Tap for more steps...
Step 18.5.1
Multiply by .
Step 18.5.2
Multiply by .