Exercises on function derivatives are essential for high school students in the United States education system. They cover a variety of concepts and calculation techniques that are at the core of the mathematics curriculum. These exercises allow students to practice independently, with hints, course reminders, and methodological advice.
For example, some exercises are aimed at high school juniors. They include calculations of derivative values at a point and polynomial function derivatives. Students also learn to derive square root functions and quotients of polynomials.
Other exercises focus on composite function derivation and products, enabling students to master more advanced differentiation techniques. Additionally, some exercises combine the calculation of derivative values at a point and the determination of the equation of the tangent to a curve, providing a practical application of theoretical concepts.
For high school seniors, some exercises focus on the use of natural logarithms and exponentials for differentiation. For example, one exercise requires deriving the function ln(x), while another explores the derivation of exponential functions.
These exercises are designed to reinforce students' understanding and prepare them for exams by providing thorough and varied practice in function derivatives.
13 exercisesExercise example N°1604 :
Calculate the derivative number of the function f(x) = `2+2*x^2` at point a = -2
derivatives of functions functions 11th Grade derivative
The aim of this corrected maths exercise is to calculate the derivative number of a function.
Exercise example N°1605 :
Let f be the function defined by f(x)= `-x-2*x^2+x^3` , calculate the derivative of f, `f'(x)`.
derivatives of functions functions 11th Grade derivative
The purpose of this exercise is to determine through the methods of algebraic calculations the derivative of a polynomial function.
Exercise example N°1606 :
Let f be the function defined by f(x)= `2*sqrt(x)` , calculate the derivative of f, `f'(x)`.
derivatives of functions functions 11th Grade derivative
The purpose of this corrected math exercise is to calculate the derivative of a square root.
Exercise example N°1607 :
Let f be the function defined by f(x)= `1/(3*x^2)` , calculate the derivative of f, `f'(x)`.
derivatives of functions functions 11th Grade derivative
The purpose of this corrected math exercise is to calculate the derivative of a quotient.
Exercise example N°1608 :
Let f be the function defined by f(x)= `1/(4-2*x+x^2)` , calculate the derivative of f, `f'(x)`.
derivatives of functions functions 11th Grade derivative
The purpose of this corrected math exercise is to calculate the derivative of a quotient and a polynomial.
Exercise example N°1609 :
Let f be the function defined by f(x)= `-3-3*x+2*x^2+x^3-5*sqrt(x)` , calculate the derivative of f, `f'(x)`.
derivatives of functions functions 11th Grade derivative
The goal of this corrected math exercise is to calculate the derivative of a polynomial and a square root.
Exercise example N°1610 :
Let f be the function defined by f(x)= `sqrt(3*x)` , calculate the derivative of f, `f'(x)`.
derivatives of functions functions 11th Grade derivative
The purpose of this corrected math exercise is to calculate the derivative of a function composed of a square root and a polynomial.
Exercise example N°1611 :
Let f be the function defined by f(x)= `(4+2*x)/(1-4*x)` , calculate the derivative of f, `f'(x)`.
derivatives of functions functions 11th Grade derivative
The goal of this exercise on functions is to calculate the derivative of a quotient of polynomials.
Exercise example N°1612 :
Let f be the function defined by f(x)= `4*sqrt(x)*(1+2*x)` , calculate the derivative of f, `f'(x)`.
derivatives of functions functions 11th Grade derivative
The purpose of this exercise on functions is to calculate the derivative of the product of a square root and a polynomial.
Exercise example N°1613 :
derivatives of functions functions 11th Grade equation_tangent_line
The purpose of this corrected math exercise is to calculate the derivative number of a function and derive the equation of a tangent to a curve.
Exercise example N°1715 :
Calculate the derivative of the function `ln(x)^5`.
neperian logarithm derivatives of functions functions 12th Grade derivative
The goal of this corrected exercise is to use the neperian logarithm to calculate the derivative.
Exercise example N°1716 :
Calculate the derivative of the function `ln(9+9*x^2)`.
neperian logarithm derivatives of functions functions 12th Grade derivative
The goal of this corrected exercise is to use the neperian logarithm to calculate the derivative.
Exercise example N°1731 :
Calculate the derivative of the function `e^(3+5*x^2)`.
exponential derivatives of functions functions 12th Grade derivative
The aim of this corrected exercise is to use the exponential for the calculation of derivatives.