Simplify the expression $p\left(x\right)=5ax^{\left(a+4\right)}+3x^ay^{\left(b-bx^{\left(b+5\right)}\right)}$

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Final answer to the problem

$p\left(x\right)=x^a\left(5ax^{4}+3y^{\left(b-bx^{\left(b+5\right)}\right)}\right)$
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Step-by-step Solution

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  • Write in simplest form
  • Solve by quadratic formula (general formula)
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Apply the property of the product of two powers of the same base in reverse: $a^{m+n}=a^m\cdot a^n$

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$p\left(x\right)=5ax^ax^4+3x^ay^by^{-bx^bx^5}$

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Learn how to solve implicit differentiation problems step by step online. Simplify the expression p(x)=5ax^(a+4)+3x^ay^(b-bx^(b+5)). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Factor the polynomial 5ax^ax^4+3x^ay^by^{-bx^bx^5} by it's greatest common factor (GCF): x^a.

Final answer to the problem

$p\left(x\right)=x^a\left(5ax^{4}+3y^{\left(b-bx^{\left(b+5\right)}\right)}\right)$

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Function Plot

Plotting: $p\left(x\right)-5ax^{\left(a+4\right)}-3x^ay^{\left(b-bx^{\left(b+5\right)}\right)}$

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7
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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

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Main Topic: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

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