Solve 2 6x - 7x + 3; 3x + 2 | 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

$$6 x ^ { 2 } - 7 x + 3 \quad 3 x + 1$$

Evaluate

$6x^{2}+2x+1$

Differentiate w.r.t. x

$12x+2$

Steps Using Derivative Rule for Sum

Multiply $3$ and $3$ to get $9$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}-7x+9x+1)$$

Combine $-7x$ and $9x$ to get $2x$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}+2x+1)$$

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 $nax^{n-1}$.

$$2\times 6x^{2-1}+2x^{1-1}$$

Multiply $2$ times $6$.

$$12x^{2-1}+2x^{1-1}$$

Subtract $1$ from $2$.

$$12x^{1}+2x^{1-1}$$

Subtract $1$ from $1$.

$$12x^{1}+2x^{0}$$

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

$$12x+2x^{0}$$

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

$$12x+2\times 1$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$12x+2$$