find the derivative of ( f(x) ).\n\n( f(x)=7 cdot 10^{x}+10 cdot 3^{x}-4 cdot 7^{x} )\n\n( f^{prime}(x)= )
find the derivative of ( f(x) ).\n\n( f(x)=7 cdot 10^{x}+10 cdot 3^{x}-4 cdot 7^{x} )\n\n( f^{prime}(x)= )
Answer
Answer:
(7\cdot10^{x}\ln10 + 10\cdot3^{x}\ln3-4\cdot7^{x}\ln7)
Explanation:
Step1: Use derivative rule for (a^{x})
The derivative of (a^{x}) is (a^{x}\ln a).
Step2: Differentiate each term
For (7\cdot10^{x}), derivative is (7\cdot10^{x}\ln10). For (10\cdot3^{x}), derivative is (10\cdot3^{x}\ln3). For (-4\cdot7^{x}), derivative is (-4\cdot7^{x}\ln7).
Step3: Combine terms
(f^{\prime}(x)=7\cdot10^{x}\ln10 + 10\cdot3^{x}\ln3-4\cdot7^{x}\ln7)