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Answer :
Final answer:
To find the derivative f'(x) of the function f(x)=x³* x⁴, we simplify it to x⁷. Differentiating x⁷ gives us f'(x)=7x⁶. Hence, the answer is (a) 7x⁶.
Explanation:
The function given is f(x) = x³⋅x⁴, and we need to find f'(x), which represents the first derivative of the function with respect to x.
We can simplify f(x) by combining the like terms, which is done by adding the exponents for the same base in multiplication:
f(x) = x³+4 = x⁷.
Now we can differentiate f(x) with respect to x:
f'(x) = d/dx ((x⁷)) = 7x⁷⁻¹ = 7x⁶
Thus, the correct answer is (a) 7x⁶.
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