Derivative of x^6*sinh(x)

Answer

6 \cdot \mathrm{sinh}\left(x\right) \cdot x^{5}+\mathrm{cosh}\left(x\right) \cdot x^{6}

Derivative of x^6*sinh(x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $x^6$ * $\sinh(x)$ : 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: $6 \cdot s$ inh(x)* $x^5$ + $\cosh(x)$ * $x^6$

The derivative of x^6*sinh(x) is 6*sinh(x)*x^5+cosh(x)*x^6.

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Derivative of x^6*sinh(x) = 6*sinh(x)*x^5+cosh(x)*x^6 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-6sinhx

How to find the derivative of x^6*sinh(x)

To find the derivative of x^6*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^6*sinh(x)?▼

The derivative of x^6*sinh(x) is 6*sinh(x)*x^5+cosh(x)*x^6.

How do you find the derivative of x^6*sinh(x)?▼

Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 6*sinh(x)*x^5+cosh(x)*x^6.

Why is the derivative of x^6*sinh(x) equal to 6*sinh(x)*x^5+cosh(x)*x^6?▼

Because differentiation measures how a function changes — applying the rules to x^6*sinh(x) yields 6*sinh(x)*x^5+cosh(x)*x^6. See the full step-by-step breakdown above.

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