Question

d/dx e⁵ˣ=......,Select Proper option from the given options.
(a) e⁵ˣ
(b) 5e⁵ˣ
(c) 5x e⁵ˣ-1
(d) 0

Answer 1

we have to find the value of $\frac{d}{dx}e^{5x}$

we know, any function y = e^f(x) is given then,
derivative of y e.g., dy/dx = e^f(x).df(x)/dx
so, use it here to solve the problem.

d/dx(e^5x) = e^{5x} × d(5x)/dx

= e^{5x} × 5

= 5e^{5x}

hence, option (b) is correct.

Answer 2

HELLO DEAR,

put y = [e^{5x}]

AND 5x = t. so y = e^t

now, dy/dx = dy/dt × dt/dx

=> dy/dx = d(e^t)/dt × d(5x)/dx

=> dy/dx = e^t × 5

=> d[e^{5x}]/dx = 5×e^{5x}


hence, option (D) is correct,

I HOPE ITS HELP YOU DEAR,
THANKS