Calculus Examples

Find the Derivative - d/d@VAR f(x)=(3x^4-8x)^3+ square root of x
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Evaluate .
Tap for more steps...
Step 2.1
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 2.1.1
To apply the Chain Rule, set as .
Step 2.1.2
Differentiate using the Power Rule which states that is where .
Step 2.1.3
Replace all occurrences of with .
Step 2.2
By the Sum Rule, the derivative of with respect to is .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Differentiate using the Power Rule which states that is where .
Step 2.5
Since is constant with respect to , the derivative of with respect to is .
Step 2.6
Differentiate using the Power Rule which states that is where .
Step 2.7
Multiply by .
Step 2.8
Multiply by .
Step 3
Evaluate .
Tap for more steps...
Step 3.1
Use to rewrite as .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
To write as a fraction with a common denominator, multiply by .
Step 3.4
Combine and .
Step 3.5
Combine the numerators over the common denominator.
Step 3.6
Simplify the numerator.
Tap for more steps...
Step 3.6.1
Multiply by .
Step 3.6.2
Subtract from .
Step 3.7
Move the negative in front of the fraction.
Step 4
Rewrite the expression using the negative exponent rule .
Step 5
Simplify.
Tap for more steps...
Step 5.1
Combine terms.
Tap for more steps...
Step 5.1.1
Multiply by .
Step 5.1.2
To write as a fraction with a common denominator, multiply by .
Step 5.1.3
Combine and .
Step 5.1.4
Combine the numerators over the common denominator.
Step 5.1.5
Multiply by .
Step 5.2
Reorder terms.