Business Calculus
Find the derivative of the function y=sin(8x4+7x−3)y=\(\sin\]\left\)(8x^4+7x-3\(\right\)).
Identify the inner function u=g(x)u = g(x)u=g(x), and the outer function y=f(u)y = f(u) y=f(u) for the composition y=f(g(x))y = f(g(x))y=f(g(x)). Then, find dydx\(\frac{\mathrm{dy}\)}{\(\mathrm{dx}\)}dxdy:
y=tan(8x4)y=\(\tan\]\left\)(8x^4\(\right\))
Determine the equation of the line tangent to the graph of y=x17−x2y=x\(\sqrt{17-x^2}\) at the point (1,4)(1, 4).
Calculate the derivative of the function g(t)=e2t+tant−4g(t)=e^{2t+\(\tan\) t-4}.
Determine the derivative of p=cos(2x2x+1)p=\(\cos\]\left\)(\(\frac{2x}{\sqrt{2x+1}\)}\(\right\)).
Given that f(−1)=−1f\(\left\)(-1\(\right\))=-1, f′(−1)=−2f^{\(\prime\)}\(\left\)(-1\(\right\))=-2, g(−1)=−1g\(\left\)(-1\(\right\))=-1, and g′(−1)=5g^{\(\prime\)}\(\left\)(-1\(\right\))=5, find the derivative of f4(x)g(x)f^4\(\left\)(x\(\right\))g\(\left\)(x\(\right\)) at x=−1x=-1.
What is the derivative of the following function?
q=4−x2q=\(\sqrt{4-x^2}\)
