10.5 Derivative of Log or Exponent that Requires Implicit
Chapter
Chapter 10
Section
10.5
Solutions 22 Videos

Differentiate each of the following.

\displaystyle y = x^{\sqrt{10}} - 3 

Q1a

Differentiate each of the following.

\displaystyle y = 5x^{3\sqrt{2}} 

Q1b

Differentiate each of the following.

\displaystyle s = t^{\pi} 

Q1c

Differentiate each of the following.

\displaystyle f(x) = x^e + e^x 

Q1d

Use the method of logarithmic differentiation to determine the derivative.

 \displaystyle y = x^{\ln x} 

Q2a

Use the method of logarithmic differentiation to determine the derivative.

 \displaystyle y = \frac{(x + 1)(x -3)^2}{(x +2)^3} 

1.22mins
Q2b

Use the method of logarithmic differentiation to determine the derivative.

 \displaystyle y = x^{\sqrt{x}} 

1.24mins
Q2c

Use the method of logarithmic differentiation to determine the derivative.

 y = (\frac{1}{x})^x 

0.58mins
Q2d

If y = f(x) = x^x, evaluate f'(e).

0.56mins
Q3a

If y = e^x + x^e, determine \frac{dy}{dx}, when x = 2.

0.39mins
Q3b

If f(x) = \frac{(x - 3)^2\sqrt{x + 1}}{(x- 4)^5}, détermine f'(7).

2.22mins
Q3c

Determine the equation of the tangent to the curve defined by y = x^{x^2} at the point where x = 2.

1.03mins
Q4

If  \displaystyle y = \frac{1}{(x + 1)(x + 2)(x + 3)} , determine the slope of the tangent to the curve at the point where x = 0.

1.26mins
Q5

Determine the points on the curve defined by y = x^{\frac{1}{x}}, x > 0, where the slope of the tangent is zero.

1.51mins
Q6

If tangents to the curve defined by y =x^2 + 4\ln x are parallel to the line defined by y - 6x + 3 =0, determine the points where the tangents touch the curve.

2.21mins
Q7 Q8 Q9 Q10

Differentiate y = x^{\cos x}, x > 0.  Make a conjecture about which number is larger: e^{\pi} or \pi^e. Verify your work with a calculator.