Solve 4x ^ 3 - 8x ^ 2 - 9x - 18 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$4x^{3}-8x^{2}-9x-18$$

Differentiate w.r.t. x

$12x^{2}-16x-9$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is $0$. The derivative of $ax^{n}$ is $nax^{n-1}$.

$$3\times 4x^{3-1}+2\left(-8\right)x^{2-1}-9x^{1-1}$$

Multiply $3$ times $4$.

$$12x^{3-1}+2\left(-8\right)x^{2-1}-9x^{1-1}$$

Subtract $1$ from $3$.

$$12x^{2}+2\left(-8\right)x^{2-1}-9x^{1-1}$$

Multiply $2$ times $-8$.

$$12x^{2}-16x^{2-1}-9x^{1-1}$$

Subtract $1$ from $2$.

$$12x^{2}-16x^{1}-9x^{1-1}$$

Subtract $1$ from $1$.

$$12x^{2}-16x^{1}-9x^{0}$$

For any term $t$, $t^{1}=t$.

$$12x^{2}-16x-9x^{0}$$

For any term $t$ except $0$, $t^{0}=1$.

$$12x^{2}-16x-9$$

Evaluate

$4x^{3}-8x^{2}-9x-18$