Calculus Examples

Find the Derivative - d/d@VAR f(x) = log base 3 of x+ square root of x
Step 1
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
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate.
Tap for more steps...
Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Combine and .
Step 6
Combine the numerators over the common denominator.
Step 7
Simplify the numerator.
Tap for more steps...
Step 7.1
Multiply by .
Step 7.2
Subtract from .
Step 8
Move the negative in front of the fraction.
Step 9
Combine and .
Step 10
Move to the denominator using the negative exponent rule .
Step 11
Simplify.
Tap for more steps...
Step 11.1
Apply the distributive property.
Step 11.2
Reorder the factors of .
Step 11.3
Factor out of .
Tap for more steps...
Step 11.3.1
Factor out of .
Step 11.3.2
Factor out of .
Step 11.3.3
Factor out of .
Step 11.4
Multiply by .
Step 11.5
Simplify the numerator.
Tap for more steps...
Step 11.5.1
Write as a fraction with a common denominator.
Step 11.5.2
Combine the numerators over the common denominator.
Step 11.6
Multiply the numerator by the reciprocal of the denominator.
Step 11.7
Multiply .
Tap for more steps...
Step 11.7.1
Multiply by .
Step 11.7.2
Use the power rule to combine exponents.
Step 11.7.3
Combine the numerators over the common denominator.
Step 11.7.4
Add and .
Step 11.7.5
Cancel the common factor of .
Tap for more steps...
Step 11.7.5.1
Cancel the common factor.
Step 11.7.5.2
Rewrite the expression.
Step 11.8
Simplify the denominator.
Tap for more steps...
Step 11.8.1
Rewrite.
Step 11.8.2
Use the power rule to combine exponents.
Step 11.8.3
Combine the numerators over the common denominator.
Step 11.8.4
Add and .
Step 11.8.5
Cancel the common factor of .
Tap for more steps...
Step 11.8.5.1
Cancel the common factor.
Step 11.8.5.2
Rewrite the expression.
Step 11.8.6
Remove unnecessary parentheses.
Step 11.8.7
Simplify.