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Find the derivative of $30-6x+2y\left(4x-5\right)$ using the definition

Step-by-step Solution

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Solution

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Final Answer

$-6+8y$
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Step-by-step Solution

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Solve the product $2y\left(4x-5\right)$

$derivdef\left(30-6x+\left(8x-10\right)y\right)$

Learn how to solve definition of derivative problems step by step online.

$derivdef\left(30-6x+\left(8x-10\right)y\right)$

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Learn how to solve definition of derivative problems step by step online. Find the derivative of 30-6x2y(4x-5) using the definition. Solve the product 2y\left(4x-5\right). Multiply the single term y by each term of the polynomial \left(8x-10\right). Find the derivative of 30-6x+8xy-10y using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is 30-6x+8xy-10y. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -6 by each term of the polynomial \left(x+h\right).

Final Answer

$-6+8y$

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 derivdef(30+-6x) using the product ruleFind derivdef(30+-6x) using the quotient ruleFind derivdef(30+-6x) using logarithmic differentiation

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Function Plot

Plotting: $-6+8y$

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a
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n
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x
y
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(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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: Definition of Derivative

Resolution of derivatives using the definition of the derivative, which is the limit of difference quotients of real numbers.

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