sin h Use the definition of the derivative and the fact that lim cos(h)-1 =1 and lim = 0 to show that if h→0 h h→0 h f(x) = sin x, then f'(x) = cos x. (Hint: sin(a + b) = sin(a) cos(b) + cos(a) sin(b))

Q: Determine the derivative with respect to 'x' of: f(x) = Cos (sin x) - sin(cos.x)

A: We know that the derivative of sinx is cosx  And cosx is -sinx

Q: (5x) S sin(x) tan(x) .........

A:

Q: 4-86 Use the formula in Exercise 83. 4. If f(4) = 5 and f'(4) =}, find (f-')'(5). 3 5. If f(x) = x +…

A:

Q: 5. Let f(x) = sin x cos x a) Determine the first derivative, and the second derivative. b) What is…

A: fx=sinxcosx

Q: Find the derivative of the given function. Infsech(x) + tanh(x)) 1) sechx+tanhr sinhx+1 sechx-tanhx…

A:

Q: (b) y = e=* + + In(3z + 1) (c) y = (cos z)° + sin(2*) (d) y = #° arcsin(2*)

A:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: Step 1: Step 2: Step 3: Step 4:

Q: y = 2 7x²)*(1 + 9x)² (sec²(x^))(tan³(x¹)) (x³ - 7x²3) 4 (1

A:

Q: 1 f(x) = x? cosx sin x + x' 4 3.

A: We will simply do the differentiation with respect to x for each term as follows

Q: The function f(r) = sinh(r) is one-to-one and so is invertible. Using our rule / formula for…

A: When the inverse of a function y=fx is f-1x then the derivative of inverse is given by…

Q: Let f (x) = sin-1(cosvx). Find f'(x).

A:

Q: The derivative of tan(9*x) is (sec(9*x))2(9))   Can you tell me where the sec2 came from?

A:

Q: Let f(x) tan-(cos(32)) f'(x) =

A:

Q: i need to find the derivative

A: Given that the function is

Q: =x sin

A: v=xsin-1(x)+1-x212 Apply product rule to take derivative for first part we know that derivative of…

Q: f(x) = 7 sinx+ 5 cos x

A:

Q: (a) y = arctan (b) y = v1-x' arsin(x)

A:

Q: 1) Find the derivative of f(x) 1+sin 2 x %3D 2 cos x

A: we are given the function is  f(x)=1+sin2x2cos3x