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Find the derivative $\frac{d}{dx}\left(x^4-x^3+7x^2+x+\frac{15}{x^2}+2\right)$ using the sum rule

Step-by-step Solution

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Final answer to the problem

$4x^{3}-3x^{2}+14x+1+\frac{-30}{x^{3}}$
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Step-by-step Solution

How should I solve this problem?

  • Find the derivative using the product rule
  • Find the derivative using the definition
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Load more...
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The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(x^4\right)+\frac{d}{dx}\left(-x^3\right)+\frac{d}{dx}\left(7x^2\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{15}{x^2}\right)+\frac{d}{dx}\left(2\right)$

Learn how to solve differential equations problems step by step online.

$\frac{d}{dx}\left(x^4\right)+\frac{d}{dx}\left(-x^3\right)+\frac{d}{dx}\left(7x^2\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{15}{x^2}\right)+\frac{d}{dx}\left(2\right)$

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Learn how to solve differential equations problems step by step online. Find the derivative d/dx(x^4-x^37x^2x15/(x^2)+2) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The derivative of the constant function (-1) is equal to zero. The derivative of the constant function (7) is equal to zero.

Final answer to the problem

$4x^{3}-3x^{2}+14x+1+\frac{-30}{x^{3}}$

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Plotting: $4x^{3}-3x^{2}+14x+1+\frac{-30}{x^{3}}$

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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

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Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

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