Differentiate -7xy³

Question

Differentiate -7xy³

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5 answers
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Answer 1

Bot answered
1 year ago

To differentiate -7xy³, we can differentiate each term separately using the power rule.

The power rule states that if we have a term of the form cx^n, where c is a constant and n is a variable with a constant coefficient, we can differentiate it by multiplying the coefficient by the exponent and then subtracting 1 from the exponent.

Let's differentiate each term separately:

Differentiating -7:
The constant -7 does not have any variables, so its derivative is 0.

Differentiating x:
The variable x has an exponent of 1, so its derivative is 1.

Differentiating y³:
The variable y has an exponent of 3, so its derivative is 3y^2.

Putting it all together, the derivative of -7xy³ is:

0x + 1(-7)y³ + (-7x)3y²
Simplifying this expression, we get:

-7y³ - 21xy²

Therefore, the derivative of -7xy³ is -7y³ - 21xy².

Answer 2

Damon answered
1 year ago

hmmm

Differentiate -7xy³
say p = -7 x y^3
then
dp = d/dx [ -7 x y^3] dx + d/dy [ -7 x y^3 ] dy
so
dp = [ -7 y^3 ] dx + [-21 x y^2 ] dy

Answer 3

Bot answered
1 year ago

Yes, that's correct! When differentiating with respect to multiple variables, we can use the partial derivative notation to indicate which variable we are differentiating with respect to. In this case, we have p = -7xy³ and we want to find dp.

Using the partial derivative notation, we have:
dp = (∂p/∂x) dx + (∂p/∂y) dy

Taking the partial derivatives, we find:
∂p/∂x = -7y³ (since ∂x/∂x = 1 and ∂y/∂x = 0)
∂p/∂y = -21xy² (since ∂x/∂y = 0 and ∂y/∂y = 1)

Substituting these results into the previous equation, we obtain:
dp = (-7y³) dx + (-21xy²) dy

So, dp = (-7y³) dx + (-21xy²) dy.

Answer 4

Step-by-Step Bot answered
1 year ago

To differentiate -7xy³, we will apply the power rule for differentiation. The power rule states that if we have a function of the form f(x) = ax^n, where "a" is a constant and "n" is a real number, the derivative of f(x) is given by:

f'(x) = nax^(n-1).

Applying this rule to -7xy³, we have:

(-7xy³)' = -7(3)(x)^(3-1)(y³)'.

Simplifying further:

(-7xy³)' = -21x²(y³)'.

Since the derivative of y³ with respect to x is zero (because y³ does not contain x), we have:

(-7xy³)' = -21x²(0).

Simplifying this expression, we get:

(-7xy³)' = 0.

Therefore, the derivative of -7xy³ with respect to x is zero.

Answer 5

Explain Bot answered
11 months ago

To differentiate the algebraic expression -7xy³, we need to apply the power rule of differentiation. The power rule states that when differentiating a term, we multiply the term by its exponent and then decrease the exponent by 1.

Let's break down the given expression step by step:

1. Start with the constant term (-7): Since it does not contain any variables, the derivative of -7 is 0.

2. Differentiate the term "x": The coefficient of "x" is 1 (since it is not explicitly written), and the exponent is 1. Applying the power rule, we multiply 1 by 1 and decrease the exponent by 1 to get 1x¹. Therefore, the derivative of x is simply 1.

3. Differentiate the term "y³": Similar to the previous step, we multiply the coefficient 1 (since it is not explicitly written) by the exponent 3 to get 1y³. We then decrease the exponent by 1 to get y². Thus, the derivative of y³ is 3y².

Putting it all together, the derivative of -7xy³ is:

0 (constant term) + 1x¹ (differentiated x) + 3y² (differentiated y³)

Therefore, the final result is 1x + 3y², or simply x + 3y².