Math / Calculus

Question $y=x^{4}+12 x \quad \frac{d y}{d x}=?$

Studdy Solution

STEP 1

1. The function $y = x^4 + 12x$ is a polynomial function.
2. The goal is to find the derivative of $y$ with respect to $x$ .
3. Standard differentiation rules, such as the power rule, will be used.

STEP 2

1. Apply the power rule to differentiate $x^4$ .
2. Apply the constant multiple rule to differentiate $12x$ .
3. Combine the results to obtain the final derivative.

STEP 3

Differentiate $x^4$ using the power rule.
$\frac{d}{d x} x^4 = 4x^3$

STEP 4

Differentiate $12x$ using the constant multiple rule.
$\frac{d}{d x} 12x = 12$

STEP 5

Combine the results from STEP_1 and STEP_2 to find $\frac{d y}{d x}$ .
$\frac{d y}{d x} = 4x^3 + 12$
Solution: $\frac{d y}{d x} = 4x^3 + 12$

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Question $y=x^{4}+12 x \quad \frac{d y}{d x}=?$

Studdy Solution

STEP 1

1. The function $y = x^4 + 12x$ is a polynomial function.
2. The goal is to find the derivative of $y$ with respect to $x$ .
3. Standard differentiation rules, such as the power rule, will be used.

STEP 2

1. Apply the power rule to differentiate $x^4$ .
2. Apply the constant multiple rule to differentiate $12x$ .
3. Combine the results to obtain the final derivative.

STEP 3

Differentiate $x^4$ using the power rule.
$\frac{d}{d x} x^4 = 4x^3$

STEP 4

Differentiate $12x$ using the constant multiple rule.
$\frac{d}{d x} 12x = 12$

STEP 5

Combine the results from STEP_1 and STEP_2 to find $\frac{d y}{d x}$ .
$\frac{d y}{d x} = 4x^3 + 12$
Solution: $\frac{d y}{d x} = 4x^3 + 12$

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Questiony=x4+12xdydx=?y=x^{4}+12 x \quad \frac{d y}{d x}=?y=x4+12xdxdy​=?

Studdy Solution

STEP 1

1. The function y=x4+12xy = x^4 + 12xy=x4+12x is a polynomial function.2. The goal is to find the derivative of yyy with respect to xxx.3. Standard differentiation rules, such as the power rule, will be used.

STEP 2

1. Apply the power rule to differentiate x4x^4x4.2. Apply the constant multiple rule to differentiate 12x12x12x.3. Combine the results to obtain the final derivative.

STEP 3

Differentiate x4x^4x4 using the power rule.ddxx4=4x3 \frac{d}{d x} x^4 = 4x^3 dxd​x4=4x3

STEP 4

Differentiate 12x12x12x using the constant multiple rule.ddx12x=12 \frac{d}{d x} 12x = 12 dxd​12x=12

STEP 5

Combine the results from STEP_1 and STEP_2 to find dydx\frac{d y}{d x}dxdy​.dydx=4x3+12 \frac{d y}{d x} = 4x^3 + 12 dxdy​=4x3+12Solution: dydx=4x3+12 \frac{d y}{d x} = 4x^3 + 12 dxdy​=4x3+12

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Question $y=x^{4}+12 x \quad \frac{d y}{d x}=?$

1. The function $y = x^4 + 12x$ is a polynomial function.
2. The goal is to find the derivative of $y$ with respect to $x$ .
3. Standard differentiation rules, such as the power rule, will be used.

1. Apply the power rule to differentiate $x^4$ .
2. Apply the constant multiple rule to differentiate $12x$ .
3. Combine the results to obtain the final derivative.

Differentiate $x^4$ using the power rule.
$\frac{d}{d x} x^4 = 4x^3$

Differentiate $12x$ using the constant multiple rule.
$\frac{d}{d x} 12x = 12$

Combine the results from STEP_1 and STEP_2 to find $\frac{d y}{d x}$ .
$\frac{d y}{d x} = 4x^3 + 12$
Solution: $\frac{d y}{d x} = 4x^3 + 12$