Derivative of x^8*sinh(x)

Answer

8 \cdot \mathrm{sinh}\left(x\right) \cdot x^{7}+\mathrm{cosh}\left(x\right) \cdot x^{8}

Derivative of x^8*sinh(x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $x^8$ * $\sinh(x)$ : use the product rule (uv)' = u'v + uv'. Each factor is differentiated once while the other is held as-is, then the two terms are added.
Differentiate each factor and combine.
Final answer: $8 \cdot s$ inh(x)* $x^7$ + $\cosh(x)$ * $x^8$

The derivative of x^8*sinh(x) is 8*sinh(x)*x^7+cosh(x)*x^8.

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Derivative of x^8*sinh(x) = 8*sinh(x)*x^7+cosh(x)*x^8 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-8sinhx

How to find the derivative of x^8*sinh(x)

To find the derivative of x^8*sinh(x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.

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Frequently Asked Questions

What is the derivative of x^8*sinh(x)?▼

The derivative of x^8*sinh(x) is 8*sinh(x)*x^7+cosh(x)*x^8.

How do you find the derivative of x^8*sinh(x)?▼

Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 8*sinh(x)*x^7+cosh(x)*x^8.

Why is the derivative of x^8*sinh(x) equal to 8*sinh(x)*x^7+cosh(x)*x^8?▼

Because differentiation measures how a function changes — applying the rules to x^8*sinh(x) yields 8*sinh(x)*x^7+cosh(x)*x^8. See the full step-by-step breakdown above.

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