Calculus Examples

Find the Derivative - d/d@VAR f(x) = square root of 8x^2+2/( square root of x)
Step 1
Rewrite as .
Tap for more steps...
Step 1.1
Factor out of .
Step 1.2
Rewrite as .
Step 2
Differentiate using the Sum Rule.
Tap for more steps...
Step 2.1
Pull terms out from under the radical.
Step 2.2
By the Sum Rule, the derivative of with respect to is .
Step 3
Evaluate .
Tap for more steps...
Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply by .
Step 4
Evaluate .
Tap for more steps...
Step 4.1
Use to rewrite as .
Step 4.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.3
Rewrite as .
Step 4.4
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 4.4.1
To apply the Chain Rule, set as .
Step 4.4.2
Differentiate using the Power Rule which states that is where .
Step 4.4.3
Replace all occurrences of with .
Step 4.5
Differentiate using the Power Rule which states that is where .
Step 4.6
Multiply the exponents in .
Tap for more steps...
Step 4.6.1
Apply the power rule and multiply exponents, .
Step 4.6.2
Cancel the common factor of .
Tap for more steps...
Step 4.6.2.1
Factor out of .
Step 4.6.2.2
Cancel the common factor.
Step 4.6.2.3
Rewrite the expression.
Step 4.7
To write as a fraction with a common denominator, multiply by .
Step 4.8
Combine and .
Step 4.9
Combine the numerators over the common denominator.
Step 4.10
Simplify the numerator.
Tap for more steps...
Step 4.10.1
Multiply by .
Step 4.10.2
Subtract from .
Step 4.11
Move the negative in front of the fraction.
Step 4.12
Combine and .
Step 4.13
Combine and .
Step 4.14
Multiply by by adding the exponents.
Tap for more steps...
Step 4.14.1
Use the power rule to combine exponents.
Step 4.14.2
To write as a fraction with a common denominator, multiply by .
Step 4.14.3
Combine and .
Step 4.14.4
Combine the numerators over the common denominator.
Step 4.14.5
Simplify the numerator.
Tap for more steps...
Step 4.14.5.1
Multiply by .
Step 4.14.5.2
Subtract from .
Step 4.14.6
Move the negative in front of the fraction.
Step 4.15
Move to the denominator using the negative exponent rule .
Step 4.16
Multiply by .
Step 4.17
Combine and .
Step 4.18
Factor out of .
Step 4.19
Cancel the common factors.
Tap for more steps...
Step 4.19.1
Factor out of .
Step 4.19.2
Cancel the common factor.
Step 4.19.3
Rewrite the expression.
Step 4.20
Move the negative in front of the fraction.
Step 5
Reorder terms.