In Exercises 59–86, find the derivative of y with respect to the given independent variable.
75. y = x³ log₁₀ x

Find the derivatives of the functions in Exercises 17–28.

y = ((x + 1)(x + 2)) / ((x − 1)(x − 2))

Suppose that the functions f and g and their derivatives with respect to x have the following values at x = 0 and x = 1.

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Find the derivatives with respect to x of the following combinations at the given value of x.

c. f(x) / (g(x) + 1), x = 1

66–71. {Use of Tech} Estimating error Refer to Theorem 8.1 in the following exercises.

66. Let f(x) = cos(x²).

b. Calculate f''(x).

66–71. {Use of Tech} Estimating error Refer to Theorem 8.1 in the following exercises.

67. Let f(x) = √(x³ + 1).

b. Calculate f''(x).

Find the derivative of each function.

$y=(3x+5)^2$

Find the derivative of each function.

$f\left(t\right)=2t(t^{-3}+t^{2/3})$

Find the derivative of the function.

$y=\frac{2-3t}{4t^2+7}$

Find the derivative of the function.

$f\left(x\right)=\frac{2x-1}{x^3+2}$