Steven Gottlieb-The AP Calculus Professor

Can You Find the Derivative of (tanx)^x?

This problem combines trigonometry, exponents, and logarithmic differentiation into one challenging AP Calculus question.

Many students know how to differentiate powers and trigonometric functions separately, but what happens when both appear in the same expression?

In this video, you'll learn:

✅ When logarithmic differentiation is required

✅ How to handle a variable in both the base and the exponent

✅ Common mistakes students make

✅ A step-by-step strategy for solving problems like this on tests and the AP Exam

Questions like this help students develop the deeper problem-solving skills needed for success in AP Calculus AB and BC.

I'm Steven Gottlieb, a retired college math professor with 35+ years of teaching college mathematics experience, and I've helped thousands of students build confidence and succeed in calculus.

🎥 Watch the video below.

👇 Before watching, see if you can solve it yourself. Post your answer in the comments!

📚 Follow this page for more AP Calculus lessons, practice problems, and exam preparation tips.

Derivative of a Definite Integral: One of AP Calculus' Most Powerful Ideas

Many AP Calculus students are surprised to learn that you can take the derivative of an integral.

This concept combines two of the biggest topics in calculus and is a direct application of the Fundamental Theorem of Calculus.

In this video, you'll learn:

✅ How to find the derivative of a definite integral

✅ When to use the Fundamental Theorem of Calculus

✅ Common AP Exam question formats

✅ Mistakes students frequently make and how to avoid them

Mastering this skill can help you solve AP Calculus problems quickly and confidently while strengthening your overall understanding of calculus.

I'm Steven Gottlieb, a retired college math professor with 35+ years of teaching college mathematics experience, and I've helped thousands of students succeed in calculus.

🎥 Watch the video below.

👇 Have a calculus question? Leave it in the comments.

📚 Interested in getting ahead in AP Calculus? Follow this page for more free lessons, tips, and practice problems.

Many AP Calculus students know how to differentiate polynomials, but get stuck when a logarithm is involved.

The good news? Once you understand the pattern, these problems become much easier and faster to solve.

In this video, you'll learn:

✅ How to find the derivative of ln(polynomial)

✅ The key logarithmic differentiation rule every AP Calculus student should know

✅ Common mistakes that cost points on tests and the AP Exam

✅ A simple approach that works every time

This is a fundamental AP Calculus topic that appears throughout the course and can show up on both multiple-choice and free-response questions.

I'm Steven Gottlieb, a retired college math professor with 35+ years of teaching experience, and I've helped thousands of students build confidence and succeed in calculus.

🎥 Watch the video below.

👇 Have an AP Calculus question? Leave it in the comments.

Struggling with converting degrees to radians in AP Calculus?
Most students don’t lose points because the concept is hard—they lose points from small setup mistakes and forgetting the conversion factor.
On exams, this shows up in trigonometric limits, derivatives, and integrals—and missing it can cost easy points.
In this video, you’ll see a clear, step-by-step method to convert quickly and accurately every time.
Message "RADIANS" and learn how we help students master AP Calculus with confidence.

Many AP Calculus students understand derivatives and integrals but struggle with trigonometric limits.

If you don't immediately recognize the key trig limit formulas, problems that should take seconds can become frustrating and time-consuming.

In this video, you'll learn:

✅ The most important trig limit every AP Calculus student must know

✅ How AP exam questions are built around this concept

✅ Common mistakes students make

✅ A simple strategy for solving these problems correctly

Understanding trig limits is an important step toward success in AP Calculus AB and BC.

I'm Steven Gottlieb, a retired college math professor, and I've spent decades helping students build the skills and confidence needed to succeed in calculus.

🎥 Watch the video below.

👇 Have a question about AP Calculus? Leave it in the comments.