Calculus Examples

Find the Derivative - d/dx y=e^(x square root of 5x-3)
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
Differentiate using the Exponential Rule which states that is where =.
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate using the Product Rule which states that is where and .
Step 4
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
Step 4.1
To apply the Chain Rule, set as .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Replace all occurrences of with .
Step 5
To write as a fraction with a common denominator, multiply by .
Step 6
Combine and .
Step 7
Combine the numerators over the common denominator.
Step 8
Simplify the numerator.
Tap for more steps...
Step 8.1
Multiply by .
Step 8.2
Subtract from .
Step 9
Combine fractions.
Tap for more steps...
Step 9.1
Move the negative in front of the fraction.
Step 9.2
Combine and .
Step 9.3
Move to the denominator using the negative exponent rule .
Step 9.4
Combine and .
Step 10
By the Sum Rule, the derivative of with respect to is .
Step 11
Since is constant with respect to , the derivative of with respect to is .
Step 12
Differentiate using the Power Rule which states that is where .
Step 13
Multiply by .
Step 14
Since is constant with respect to , the derivative of with respect to is .
Step 15
Combine fractions.
Tap for more steps...
Step 15.1
Add and .
Step 15.2
Combine and .
Step 15.3
Move to the left of .
Step 16
Differentiate using the Power Rule which states that is where .
Step 17
Multiply by .
Step 18
To write as a fraction with a common denominator, multiply by .
Step 19
Combine and .
Step 20
Combine the numerators over the common denominator.
Step 21
Multiply by by adding the exponents.
Tap for more steps...
Step 21.1
Move .
Step 21.2
Use the power rule to combine exponents.
Step 21.3
Combine the numerators over the common denominator.
Step 21.4
Add and .
Step 21.5
Divide by .
Step 22
Simplify the expression.
Tap for more steps...
Step 22.1
Simplify .
Step 22.2
Move to the left of .
Step 23
Combine and .
Step 24
Simplify.
Tap for more steps...
Step 24.1
Apply the distributive property.
Step 24.2
Simplify the numerator.
Tap for more steps...
Step 24.2.1
Simplify each term.
Tap for more steps...
Step 24.2.1.1
Multiply by .
Step 24.2.1.2
Multiply by .
Step 24.2.2
Add and .
Step 24.2.3
Apply the distributive property.
Step 24.2.4
Rewrite using the commutative property of multiplication.
Step 24.2.5
Move to the left of .
Step 24.2.6
Reorder factors in .
Step 24.3
Reorder terms.
Step 24.4
Factor out of .
Tap for more steps...
Step 24.4.1
Move .
Step 24.4.2
Factor out of .
Step 24.4.3
Factor out of .
Step 24.4.4
Factor out of .