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Mixed Differentiation

Mixed Differentiation Problems 1

We assume that you have mastered these methods already.

• Basic Derivatives for raise to a power, exponents, logarithms, trig functions
• Multiple Rule
• Sum and Difference Rule
• Product Rule
• Quotient Rule
• Chain Rule
• Logarithmic Differentiation
• Algebraic manipulation to write the function so it may be differentiated by one of these methods

These problems can all be solved using one or more of the rules in combination.

The next example shows the application of the Chain Rule differentiating one function at each step. Not surprisingly the end result is the same.

Example

Find the derivative of y = sin(ln(5x² − 2x))

This way of writing down the steps can be handy when you need to deal with using the Chain Rule more than once or when you need to use a mixture of methods.

Exercises

For each function obtain the derivative.

1. y = 12x⁵ + 3x⁴ + 7x³ + x² − 9x + 6
2. y = sin (5x³ + 2x)  
3. y = x²sin 2x
4. y = x⁴(sin x³ − cos x²)
5. y = e^{3x − 2}

Check first 5 answers (this will open a new window)

6. y = 4xe^2x − 9x
7. y =  
8. y =  
9. y =  ln sin 5x³
10. y =  

Check next 5 answers (this will open a new window)

11. y = 4xe^−5x
12. y = 10^{(cos x) −10x}
13. y = 4e^x(1 + ln x)(sin x)
14. y = e^xln (5x³ + x²)
15. y =

Check next 5 answers (this will open a new window)

16. y = (cos x)(1 − sin²x)
17. y = 5^xe^{2 + 5x}
18. y = cosec 3x
19. y = ln (4e^3x)
20. y =

 Check last answers (this will open a new window)

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