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# Find the derivative of $\left(x+1\right)\left(x-4\right)$

## Step-by-step Solution

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$x-4+x+1$
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##  Step-by-step Solution 

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1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x+1$ and $g=x-4$

$\frac{d}{dx}\left(x+1\right)\left(x-4\right)+\left(x+1\right)\frac{d}{dx}\left(x-4\right)$
2

The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\left(\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(1\right)\right)\left(x-4\right)+\left(x+1\right)\frac{d}{dx}\left(x-4\right)$
3

The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\left(\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(1\right)\right)\left(x-4\right)+\left(x+1\right)\left(\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(-4\right)\right)$
4

The derivative of the constant function ($1$) is equal to zero

$\frac{d}{dx}\left(x\right)\left(x-4\right)+\left(x+1\right)\left(\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(-4\right)\right)$
5

The derivative of the constant function ($-4$) is equal to zero

$\frac{d}{dx}\left(x\right)\left(x-4\right)+\left(x+1\right)\frac{d}{dx}\left(x\right)$

The derivative of the linear function is equal to $1$

$1\left(x-4\right)$

Any expression multiplied by $1$ is equal to itself

$x-4$
6

The derivative of the linear function is equal to $1$

$x-4+\left(x+1\right)\frac{d}{dx}\left(x\right)$

The derivative of the linear function is equal to $1$

$1\left(x-4\right)$

Any expression multiplied by $1$ is equal to itself

$x-4$

The derivative of the linear function is equal to $1$

$1\left(x+1\right)$

Any expression multiplied by $1$ is equal to itself

$x+1$
7

The derivative of the linear function is equal to $1$

$x-4+x+1$

$x-4+x+1$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of (x+1)(x-4) using the product ruleFind derivative of (x+1)(x-4) using the quotient ruleFind derivative of (x+1)(x-4) using logarithmic differentiationFind derivative of (x+1)(x-4) using the definition

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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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