Find the derivative of the given function.f(x)=2x−5xf(x)=2^x-5^xf(x)=2x−5x

2xln⁡2−5xln⁡$$52^{x}$$\$$ln2-5^{x}$$\ln52xln2−5xln5

Find the derivative of the given function. f ( x ) = 2 x − 5 x f(x)=2^x-5^x f ( x ) = 2 x − 5 x

In this problem, we wanna find the derivative of the function f of x equals 2 to the x minus 5 to the x. Now we just learned that the derivative of a general exponential function, so ddx of some base b to the power of x, is going to be that b to the power of x times the natural log of that base b. Now since here I have one exponential function being subtracted from another, that means I can look at each of their derivatives individually and just subtract them using the difference rule for derivatives. So my derivative here, f prime of x, using this rule that we just learned over here focusing on that 2 to the x, this is going to be 2 to the x times the natural log of 2. Then I'm going to subtract the derivative of 5 to the x, which is going to be 5 to the x times the natural log of 5, again, just using that rule. So this is my full derivative here. Let me know if you have any questions, and let's keep going.