Solve - 3x + 4x + y + 3x + 3y - 4x | 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

$$-3x+4x+y+3x+3y-4x$$

Evaluate

$4y$

Solution Steps

Combine $-3x$ and $4x$ to get $x$.

$$x+y+3x+3y-4x$$

Combine $x$ and $3x$ to get $4x$.

$$4x+y+3y-4x$$

Combine $y$ and $3y$ to get $4y$.

$$4x+4y-4x$$

Combine $4x$ and $-4x$ to get $0$.

$$4y$$

Differentiate w.r.t. y

$4$

Steps Using Definition of a Derivative

Combine $-3x$ and $4x$ to get $x$.

$$\frac{\mathrm{d}}{\mathrm{d}y}(x+y+3x+3y-4x)$$

Combine $x$ and $3x$ to get $4x$.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4x+y+3y-4x)$$

Combine $y$ and $3y$ to get $4y$.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4x+4y-4x)$$

Combine $4x$ and $-4x$ to get $0$.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4y)$$

The derivative of $ax^{n}$ is $nax^{n-1}$.

$$4y^{1-1}$$

Subtract $1$ from $1$.

$$4y^{0}$$

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

$$4\times 1$$

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

$$4$$