Differentiate the function

Question

f(x)=x^5+5^x

Answer 1

f(x) = x⁵ + 5^x

Apply 'derivative with respect to x' each side.

f'(x) = (d/dx)[x⁵ + 5^x]

f'(x) = (d/dx)x⁵ + (d/dx)5^x

Power Rule of Derivative: (d/dx)xⁿ = nx^n-1

And Derivative of Exponential Functions: (d/dx)(a^x) = a^xlog(a)

f'(x) = 5x^5-1 + 5^xlog(5)

f'(x) = 5x⁴ + 5^xlog(5)

Therefore the derivative of f(x) is 5x⁴ + 5^xlog(5).