Calculus 1 Formula Sheet-Questions and Answers Graded A+

Calculus 1 Formula Sheet-Questions and Answers Graded A+ d/dx k - ANSWER-0 d/dx (mx+b) - ANSWER-m d/dx (x^n) - ANSWER-nx^n-1 d/dx [f(x)/g(x)] - ANSWER-g(x)f'(x)-f(x)g'(x)/g(x)^2 d/dx [f(x)+g(x)] (Sum Rule) - ANSWER-f'(x)+g'(x) d/dx (f(x)-g(x)) - ANSWER-d/dx f(x) - d/dx g(x) d/dx [f(x)g(x)] - ANSWER-f'(x)g(x)+f(x)g'(x) d/dx a^x - ANSWER-a^x ln(a) A function is not differentiable if - ANSWER-- discontinuity - corner (limit from left ≠ limit from right) - vertical tangent Difference Quotient - ANSWER-f(x+h)-f(x)/h s'(t)= - ANSWER-v(t) v'(t)= - ANSWER-a(t) d/dx f^-1(x) (inverse) - ANSWER-1/f'(f^-1(x)) Derivative of Cosine - ANSWER--sinx derivative of sine - ANSWER-d/dx(sinx)=cosx d/dx [ln|x|] = - ANSWER-1/x d/dx [log_a X] = - ANSWER-1/xlna d/dx arctan(x) - ANSWER-1/(1+x^2) d/dx arcsin(x) - ANSWER-1/sqrt(1-x^2) Chain Rule - ANSWER-f'(g(x))g'(x) derivative of tanx - ANSWER-sec^2x Inverse Derivative Formula - ANSWER-1/f'(f^-1(x)) sin^2x+cos^2x - ANSWER-=1