Higher-order Derivatives

Third and Higher Order Derivatives


For the function f(x)=ex(7sinx+3cosx),f(x)=e^x(7\sin x+3\cos x), what is the third derivative f(x) f'''(x)?

What is the 19th19 ^{th} derivative of 13e3x?\displaystyle \frac{1}{3}e^{3x}?

If f(x)=2x415x3+15x17,f(x)=2x^4-15x^3+15x-17, what is the value of limx1f(x)+66x1?\displaystyle \lim_{x \to 1} \frac{f''(x)+66}{x-1}?

What is the third derivative of the function y=8sinxy=8\sin x with respect to xx?

If f(x)=e5x,f(x)=e^{5x}, what is the value of f(0)?f'''(0)?


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