Derivative of sinh(5x)

Answer

5 \cdot \mathrm{cosh}\left(5 \cdot x\right)

Derivative of sinh(5x)

Rule Used: Chain Rule
Steps: Identify a composite function in $\sinh(5 \cdot x)$ : use the chain rule $\frac{d}{dx} f(g(x))$ = f'(g(x))·g'(x). The inner derivative is required because a stretch or shift of the input changes how fast the output moves.
Differentiate the outer function, then multiply by the inner derivative.
Final answer: $5 \cdot c$ osh( $5 \cdot x$ )

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

Instant step-by-step solution for sinh(5x)

Derivative TrigonometricIntermediate

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Derivative of sinh(5x) = 5*cosh(5*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sinh5x

How to find the derivative of sinh(5x)

To find the derivative of sinh(5x), 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 sinh(5x)?▼

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

How do you find the derivative of sinh(5x)?▼

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

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

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

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