Derivative of $\sinh\left(x\right)$
Differentiated with respect to x. Edit the function · Differentiation rules
Step-by-step solution
Input function
$$\sinh\left(x\right)$$
Start of the differentiation
$$\frac{d}{dx}{\left[\sinh\left(x\right)\right]}$$
Yellow: the expression being replaced. Green: its replacement.
Step 1 — Derivative of the hyperbolic sine
Differentiation rule
📖 Rule
$$\frac{d}{dx}\sinh\left(x\right)=\cosh\left(x\right)$$
Why: The argument is exactly x. Apply the known elementary derivative.
🧮 Current expression
$$\bbox[#fff1b8, padding:0.15em]{{\color{black}{\vphantom{\dfrac{d}{dx}}\,\frac{d}{dx}{\left[\sinh\left(x\right)\right]}\,}}}$$
✨ After: Derivative of the hyperbolic sine
$$\bbox[#d6f5df, padding:0.15em]{{\color{black}{\vphantom{\dfrac{d}{dx}}\,\cosh\left(x\right)\,}}}$$
Final result
$$\cosh\left(x\right)$$
Cross-check with a computer algebra system
The derivative computed directly by the computer algebra system Maxima:
$$\cosh\left(x\right)$$
Step-by-step result ↔ Maxima: identical ✓