</script>

Figure 17 | Writing code for a website based on user request. The model follows the instructions and
requirements defined by the user and converts them to functioning code.

56

Gemini: A Family of Highly Capable Multimodal Models

9.4.2. Mathematics: Calculus

Prompt
Find the derivative of sinh 𝑥 + cosh 𝑦 = 𝑥 + 𝑦.
Model Response (rendered latex)
We have that 𝑑

𝑑𝑥 sinh 𝑥 = cosh 𝑥 and 𝑑

𝑑𝑥 cosh 𝑦 = sinh 𝑦 𝑑 𝑦

𝑑𝑥 . Therefore,

cosh 𝑥 + sinh 𝑦

𝑑 𝑦

𝑑𝑥 = 1 + 𝑑 𝑦

𝑑𝑥

.

Solving for 𝑑 𝑦

𝑑𝑥 , we find that

𝑑 𝑦
𝑑𝑥 =
Final Answer: The final answer is 1−cosh 𝑥
sinh 𝑦−1.

1 − cosh 𝑥
sinh 𝑦 − 1 .

Figure 18 | Solving a calculus problem. The model is able to get a solution to a calculus problem with
step-by-step explanation and correctly defined LaTeX equations.
Source: question is provided by Macmillan Learning.

57

Gemini: A Family of Highly Capable Multimodal Models

9.5. Multi-step reasoning and mathematics
gemini_1_report