Derivatives of Functions: Problems with Solutions

By Denitsa Dimitrova (Bulgaria)
Problem 1
Find the first derivative of the function
$y=5x-4$
Problem 2
Find the derivative of the function
$y=-x^3+4x^2-5$
Problem 3
Find the derivative of the function
$y=(x-1)(x^2+3)$
Problem 4
Find the derivative of the function
$y=(x+2)^2-3x^3$
Problem 5
Find the derivative of the function
$y=\frac{5+x}{x-3}$
Problem 6
Find the derivative of the function
$y=(x^2-3x+\sqrt{2})^5$
Problem 7
Find the first derivative of the function
$y=\frac{x^2-3x}{x^2+1}$
Problem 8
Find the first derivative of the function
$y=\sqrt{x^2-3}$
Problem 9
Find the first derivative of the function
$y=\left(\frac{2-x}{x+3}\right)^2$
Problem 10
Find the first derivative of the function
$y=x(x^2-3)(x^2+1)$

Problem 11
Find the first derivative of the function
$y=x^3\cos x$
Problem 12
Find the first derivative of the function
$y=\frac{1-\cos x}{1+\cos x}$
Problem 13
Find the first derivative of the function
$y=\sqrt{7x-x^2-12}$
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