find derivative
y= (3x^5-6x^3)/7secx
Use the quotient rule
dy/dx = [7secx (15x^4 - 18x^2) - (3x^5 - 6x^3)(7secxtanx) ]/(49 sec^2 x)
simplify as needed.
i can not simplify further.
To find the derivative of the given function y = (3x^5 - 6x^3)/(7secx), we can use the quotient rule. The quotient rule states that if we have a function in the form f(x)/g(x), where f(x) and g(x) are differentiable functions, then the derivative of the function is given by:
(dy/dx) = (g(x)*(d/dx)[f(x)]) - (f(x)*(d/dx)[g(x)]) / (g(x))^2
Now let's find the derivative step-by-step:
Step 1: Identify f(x) and g(x)
In our case, f(x) = 3x^5 - 6x^3 and g(x) = 7secx.
Step 2: Find the derivatives of f(x) and g(x)
Let's find the derivative of f(x) first:
(d/dx)[f(x)] = 15x^4 - 18x^2
Now, let's find the derivative of g(x) using the chain rule for secx:
(d/dx)[g(x)] = (d/dx)[7secx]
= 7 * (d/dx)[secx]
To find the derivative of secx, we can use trigonometric identities. The derivative of secx is secx * tanx.
Therefore, (d/dx)[g(x)] = (7 * secx * tanx)
Step 3: Apply the quotient rule formula
(dy/dx) = [(g(x) * (d/dx)[f(x)]) - (f(x) * (d/dx)[g(x)])] / (g(x))^2
= [(7secx)(15x^4 - 18x^2) - (3x^5 - 6x^3)(7secx * tanx)] / (7secx)^2
Simplify further if needed, but this is the derivative of y = (3x^5 - 6x^3)/(7secx).