(1 pt) If f(x) = x8 sin (x), the derivative of f with respect to X is f (x)- Note: the best way to enter trig functions, for example cos(ar b) is to use parentheses: cos(ax+b).
Find the range of the following functions Please solve without using calculus (vii) f(x)sin (sin x) (viii f(x) cos (cos x) (ix) f(x)sin (sin x)cos (sinr) (x) f(x) cos (sin x)sin (cos x) (vii) f(x)sin (sin x) (viii f(x) cos (cos x) (ix) f(x)sin (sin x)cos (sinr) (x) f(x) cos (sin x)sin (cos x)
Find the derivatives of the following functions. a) f(x) = sin(x²) b) g(x) = ln(cos(x)) c) h(z) – In(1002? + 47x)? d) k(z) = resin(2)
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
Consider the following functions. f(x)=1/x and g(x)= x^3 Find the formula for (f∘g)(x) and simplify your answer. Then find the domain for (f∘g)(x) . Round your answer to two decimal places, if necessary. Also, Find the formula for (g∘f)(x) and simplify your answer. Then find the domain for (g∘f)(x) . Round your answer to two decimal places, if ny.
The hyperbolic cosine and hyperbolic sine functions, f(x) cosh(x) and g(x) sinh(), are analogs of the trigonometric functions cos(x) and sin(z) and come up in many places in mathematics and its applications. (The hyperbolic cosine, for example, describes the curve of a hanging cable, called a catenary.) They are defined by the conditions cosh(0)-l, sinh(O), (cosh())inh("), d(sinh()- csh) (a) Using only this information, find the Taylor polynomial approximation for cosh(x) at0 of COS degree n = 4. (b) Using only...
Express the general solution of the given system of equations in terms of real-valued functions sin 4t - cos 4t - sir 4t cos 4t sin 4t -cos 4t 4 sin 5t -cos 5 4 sin 4t cos 4t Find the solution of the given initial value problem. Describe the behavior of the solution as t 00 x, x (0) 2 -3 Enclose arguments of functions in parentheses. For example, sin (2) Do not simplify trigonometric functions of nt, where...
4. [-12 Points] DETAILS OSPRECALC1 7.2.052. Rewrite in terms of sin(x) and cos(x). sin(x + **) Additional Materials eBook Sum and Difference Identities for Sine Submit Answer 5. [-12 Points] DETAILS OSPRECALC1 7.2.060. Simplify the given expression. sin(5x) cos(7x) - sin(7x) cos(5x) Additional Materials eBook Sum and Difference Identities for Sine 6. [-12 Points] DETAILS OSPRECALC1 7.2.062. Given that sin(a) = } and cos(b) = - , with a and b both in the intervaller find the exact values of...
Let f(x)=x2+4 and g(x)=3x−6. Find a formula for f(g(x)) in terms of x.
Consider the following function. f(x) = cos(x) - sin(x), (0, 2) (a) Find the critical numbers of f, if any. (Enter your answers as a comma-separated list.) (b) Find the open intervals on which the function is increasing or decreasing (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing х decreasing X (c) Apply the First Derivative Test to identify all relative extrema. (If an answer does not exist, enter DNE.) relative minimum (X,Y)...